Can a tenure-track job candidate infer any meaning from the response to an initial contact email? I'm on the job market for tenure-track positions in mathematics in the US this application cycle. I was advised by various people to contact the people in the institutions that I would really like to go to, so I have just contacted 4-5 top institutions that I am planning to apply to.

In the usual job market desperation, I may try to decipher every word in their response (if they respond at all), so I am curious about if there is anything to be deciphered at all. I'm only a postdoc and I have not had emails of this sort, but I can see myself responding in various ways.

For example, for a complete no-name who has no chance in my school, maybe the kindest thing is just to thank them, ignore them, or just tell them that we're not hiring in their area.

Maybe if it's someone that looks like they have a shot, maybe I'd respond telling them that I'll read their applications carefully, or something along those lines. Or maybe I'll volunteer some extra information such as our intended area of hire (because those generally don't appear in job ads) or actually pass on the email to the hiring committee.

Or, do you just have a canned response that you send out to everyone who contacts you?

All of this is speculation, and I'm intentionally doing this before getting any response back, so that I don't go crazy over the responses.

Does what I say above have any similarities with the reality? Even a glimmer of hope from any of the responses will put my mind at ease, so I am hoping for many anecdotal stories from current/past faculty who have had to deal with emails of this sort, which I am sure they receive plenty of.
Don't stress out about the responses, since it's nearly impossible to get reliable information by reading between the lines.  The variation in how people might respond is enormous, and unless you really know the people involved it's hard to know what it means.  For example, suppose someone sends a friendly, encouraging reply.  Maybe it means you have a real shot at the job.  Maybe it means they think you have a real shot, but they could be totally wrong.  (Sometimes people on hiring committees have unrealistic beliefs about how everything will play out.)  Maybe it's just their personality and has nothing to do with your chances.  Maybe they are deliberately saying the same thing to everyone in order to avoid awkwardness.  If you don't know them pretty well, all you can do is guess.  Of course a standoffish reply is equally difficult to interpret.  The net effect is that you'll get replies that look like they may contain information, but you really won't know what, if anything, they mean.  It's best to resign yourself to this now, rather than spending a lot of time worrying over how to interpret replies and not actually learning anything valuable in the process.