I was going to answer and then realised I wasn't entirely sure, as I am never without a connection and couldn't definitively answer, but you can definitely play without buying it, but it is a rather old and outdated version, so a lot of features arent in it.
Try this support question on the minecraft.net site, I think this answers what you need to know.
Mojang | Can I try Minecraft before I buy it?-
If you buy the game, you can download it and play it from your hard drive, or alternatively just use the free version in a similar way.