I can tell you for a fact that the Samsung Galaxy S3 can move to T-Mobile, as it is a CDMA and GSM compatible phone. I had one on Verizon and moved it to T-Mobile last year by buying a SIM and setting my prepaid plan up online. $31.80/month with tax for 100 talk minutes, unlimited text and more data than you'll use.
Not sure about the Note, but seeing as that is also a Samsung I'd be inclined to say it's good. Never having used one, try this: Go into Settings > More Settings > Mobile Networks > Network Mode and see what the settings are (this is the trail for the S3). My S3 has three options. Global (what I use), LTE/CDMA and GSM/UMTS. If this is also true of the Note, switch it to Global and go where you want.