"Dumb question: Does the music signature tell if the song can fit with a particular dance?"

Sort of. The time signature alone does not, but the time signature plus all the supporting markings and tradition that a musician would use to understand what it practically means will get you close.

What remains is the interpretive sense of the difference between a combination of music & dance that is theoretically possible, as compared to one that is sensible. On a few occasions you will find a combination that is possible, but just doesn't make any sense. Also you will occasional encounter one that doesn't seem like it should be possible, but turns out to make wonderful sense as soon as you see someone dancing (a show for example) to it.