If I install a ROM that doesn't exactly match my phone, will it work at all?
The answer is almost definetly no.

Although there might not be much difference between the models, there are bits that are different. These bits won't work. Other bits may depend on these bits, and they won't work either. The baseband and radios might work fine, but the rest of the mismatched components will lead to, at best, a soft brick. I have a Moto G LTE second gen, and accidentally flashed a ROM from its non-LTE brother. Almost exactly the same apart from the radio, and a different model number of processor (both Snapdragon 400s though). I ended up with a brick that was very hard to sort out (not helped by the fact my nandroid backup was corrupted).

Also (correct me if I'm wrong), I believe that a number of ROMs will refuse to flash if they detect the wrong device. I found that out when an old copy of TWRP kept feeding a zip the wrong information. Don't try and test it out though :)

In short, flashing ROMs on devices they weren't intended to be flashed with is a bad idea, no matter how similar in specs they may seem.