I recently ran into this problem, and the short answer is some work - some don't - good luck.
GSM now comes in a lot of frequencies.
To know if a phone will work on a given GSM network, you need to know the frequencies that network supports, and the frequencies the phone supports. Good luck looking those up, but it can be done, but _has_ to be done for all networks and all phones.
If you can't attach to the data network, you can't authenticate a sim, and you can't receive phone calls.
For example, I had my Moto G US in the UK. It turns out the Moto G UK does not support the 2.1Ghz band, but does support 1.8Ghz. Therefore it can exist on Vodophone and O2 and MVNOs of those networks. It can't exist on 3 (the network). My fail to buy a SIM card on 3, which didn't work. I can't tell what Lycamobile uses - most people said Vodaphone - but I was unsure.
If your phone supports 1.8Ghz, as the Moto US versions do, you'll be able to attach to SOME GSM network. It's a very popular frequency. If you get the Moto Global version, it'll cover some other really popular new frequencies, but not the 1.9 that TMobile uses. However, your best way of figuring out if the phone works is to search for network operators in the area you're in. If you see the network operator in your phone's list, the phone can attach to it, and you should buy a sim.
I'm not even sure I'm right about what TMobile uses, what with the "re-farming" and everything.
Talking to someone at a cell phone store will be a source of frustration. They don't know the frequencies their network uses. They don't know what your phone supports. You'll just have to do your legwork before you go to a country.
I overheard one cell phone store employee stating falsehoods to one potential customer. I also couldn't buy a Vodaphone SIM - "the system for selling data sims is down" - for two days in the UK, never did buy one. Don't know what's up with that.
Short answer is: no guarantees, but the US phone with 1.8Ghz should give you options, but do your own research - check the frequencies of the phone, check the frequencies of the carriers, in the areas you plan to travel, and expect to get stranded once in a while.