You can safely try the speaker in the inverted setup to see if it sounds good that way. If the speaker was designed to be used with the woofer below, even if you maintain the same tweeter height and axis, the sound will be different because the distance between the woofer to the floor (at to the ceiling) has changed. That change in distance will affect the frequency at which the woofer's sound bouncing off the floor will interact with the direct signal from the woofer (the floor bounce path is longer, so the interaction means the two paths are partially out of phase). Some designers account for floor bounce in the design of the crossover, or various things are done to voice the speaker correctly which at least partially takes into account floor bounce.
odd question about stand-mount speakers
Is there any reason you shouldn't turn stand-mount speakers upside down and listen to them that way, as long as you use some kind of vibration control/decoupler between the speakers and the surface they're placed on? The reason I ask is because, at least in a near-field setup, I would think having the mid/woofer ABOVE the tweeter would enhance image height/size -- assuming the tweeter is kept at ear level. (A couple of asides: I don't currently have bookshelf speakers, otherwise I would experiment. Will likely be buying some in the near future though. Also, I know that there are some stand-mount speakers that place the mid/woofer above the tweeter, but the vast majority do not -- most of the ones I'm interested in do not.)