Can you really hear the "time" of a song?

Oh, boy. I didn’t want to bring this up in this thread quite yet, (as I was afraid of confusing the OP) but here’s some more examples from a recent Straight Dope thread I put up:

The 3/4 and 4/4 examples should be most useful for the OP at the moment. Disregard the 12/8 and the 5/8 unless you’re curious.