Q:

Can viewfinder type make an appreciable difference in manual focus?

I have a few old vintage lenses that I love to shoot with on my Canon T3.
The obvious disadvantage is the challenge of getting sharply focuses images while focusing manually. I have great vision, but I still struggle to focus sharply.
Will getting a camera with a larger viewfinder have any appreciable improvement in ones ability to discern focus from what they see in the viewfinder?
Will going from pentaprism to pentamirror have any appreciable effect?
I hope this is not too subjective. I am looking at a used canon 7D which has a much more magnified viewfinder over the T3 and is pentaprism instead of pentamirror.

A:

A larger viewfinder might help slightly, but probably not as much as you hope. You probably won't notice any difference in focusing ability between a pentamirror and pentaprism.
The best way to increase your manual focusing ability is to replace your camera's focusing screen with one that has split prism and microprism focusing aids, just like the ones you used to have in film cameras.
Note that installation of a different focusing screen will probably affect  your camera's exposure metering system.
See also:

What is a focusing screen?
Do focusing screens exist for modern DSLRs?
Why don't DSLRs come equipped with "classic" focusing screens (split prism, etc)?
Disadvantages of split-prism focusing screens?
Can a new focusing screen affect exposure metering?
How do you manually focus accurately without a focusing screen?

A:

Absolutely, yes.  But possibly not in the way you're thinking.

The obvious disadvantage is the challenge of getting sharply focuses images while focusing manually. I have great vision, but I still struggle to focus sharply.

You can change the type of focus screen with some dSLR models and that can add some focus aids like split-circles and prism collars; it was one of the many reasons I upgraded to an 50D from a 350D/XT back when Canon still put interchangeable focus screens in the XXDs (before LCD overlays happened).  But you still need good eyesight.

Will getting a camera with a larger viewfinder have any appreciable improvement in one's ability to discern focus from what they see in the viewfinder? Will going from pentaprism to pentamirror have any appreciable effect?

A bit. I have a 5DMkII as well as my 50D, and while the 5DMkII has a bigger, brighter viewfinder, and with the precision-matte focus screen, I can actually focus my adapted OM Zuiko 50mm f/1.2 when wide open accurately, since DoF is now depicted accurately. But it's not necessarily a huge amount of difference between that and my 50D equipped with a split/circle prism collar focus screen. 

I am looking at a used canon 7D which has a much more magnified viewfinder over the T3 and is pentaprism instead of pentamirror.

The 7D's viewfinder won't be that much larger than the T3's, but it will be a little brighter.
But your best bet is an...
Electronic viewfinder
Mirrorless cameras have electronic viewfinders: ones that show the image the same way the LCD on the back of the camera does. But because it's digital data, the image can be manipulated.  Exposure simulation is possible. As are manual focus aids, such as focus peaking, simulated split-screen, and magnification can all be used to help nail manual focus.  Both my Fuji X100T and Panasonic GX-7 camera bodies have these types of features, and I find it slightly easier to use them than my alternative viewscreens in my dSLRs to manually focus my adapted manual lenses.
On a Canon dSLR, you can do some of this with the LCD, with the Magic Lantern firmware add-on, but it's not as convenient as having these features in the viewfinder.

A:

The 7D viewfinder is significantly larger and brighter than the T3's. The T3 has 0.8X magnification of 95% of an APS-C sensor. The 7D has 1.0X magnification of 100% of the same sized sensor. That's about 16.95x11.3 mm for the T3 compared to 22.3x14.9 mm for the 7D. That's a 4:3 ratio in size! The 7D's pentaprism is also noticeably brighter than the pentamirror found on the T3.
Even a 33% increase in viewfinder size and an increase in brightness are only going to be incremental improvements, though. Back in the manual focus dark ages we had additional focusing aids in the viewfinder. Some current DSLRs have interchangeable focusing screens that include the option to add some of those long-lost focusing aids back to the viewfinder. Even cameras with officially non-interchangeable screens, such as the 7D, can be modified but it requires a bit more intricate work. There are third party companies that will sell and install a more traditional style of focusing screen in many DSLRs including the 7D.
Our digital cameras often give us focusing assistance in other ways that we don't often realize. Even when manually focusing, there are often focus confirmation lights in the viewfinder that let us know when a selected AF point is in focus. Unfortunately, to use the focus confirmation light with Canon EOS cameras when manually focussing, the camera must detect a lens attached. If the adapter you are using doesn't report its presence to the camera via the electrical contacts on the lens mounting flange, that option will not be available with any EOS camera. You might try to find a "chipped" adapter for the particular mount you are adapting to the Canon EOS EF-mount.
Another option is a camera with an electronic viewfinder than offers EVF-only features such as focus peaking. Since you are already in the Canon EOS ecosystem, the EOS M5, which uses the EF-M mount, might be an option to consider. It has the same 24.2 MP APS-C sensor that is found in the EOS 80D. Although the registration distance (often called the "flange-focal distance") is shorter for the mirrorless EF-M series than the EF/EF-S mount, the electronic communication protocols are all the same between the EOS M-series and other EOS cameras. With a standard Canon-made adapter, any EOS EF/EF-S lens can be used on an EOS-M camera without the drawbacks often associated with adapted lenses. Many other Canon accessories, such as TTL flashes, are also fully compatible with the EOS-M line.
In addition to being able to use EF/EF-S lenses and any lenses adaptable to your T3, the shorter 18mm registration distance of the EF-M mount also opens up the possibility of using adapted lenses from other systems with registration distances too short to be adaptable to the EF/EF-S mount with its 44mm registration distance.

