No -- the limiting factor is the USB3 port on the drive, not the Thunderbolt port on the system.  Unless you have a Thunderbolt drive (which really comes into its own only if it's an SSD as opposed to a hard drive), there won't be any difference.  
I bought a WD My Passport to back up my laptop using Acronis, but when connecting the drive via the usb-c port on the computer, the backup always fails. I do have a cable that goes from USB-C to USB-A & the backup will run fine with that, but I thought USB-C would be a faster transfer rate. The log from Acronis shows 543.3 Mbps, would C be faster and why does it have a problem with connecting to that C port? I've been asked if that port is meant for a docking station - is it?  
USB-C port on XPS 9560