I've done it with the N900A, the AT&T version (the ROM had to be modified, of course, because the A has a locked bootloader) so I can't see any problem.
EXCEPT - downdating past a major rev. IOW, 4.4.4 to 4.4.2 is no problem. 5 to 4 may be. Check with the developers at
T-Mobile Galaxy Note 3 Android Development - XDA Forums first. I'm sure some of them have done it, and they can tell you whether it's something you can't recover from. (When you're a developer, you expect to destroy a few phones.)
To be sure, have a copy of an N900W8 ROM ready to flash if it goes sideways. (
SamMobile Firmwares if you don't have one - and you'll have to create a free account to download the file.)
Read
[Samsung] How to flash Stock ROM via ODIN if you're not familiar with Odin.
(The first time your phone doesn't start up, you panic. The 100th time it doesn't start up, you kick yourself for doing something so stupid and wasting time, then you flash a working ROM - and die of boredom. Watching grass grow in the winter is more exciting and pushing your hair back into place is more scary.)
My GPS wasn't working yesterday, the first time I tried it since trying to flash an old modem (I think that's what caused it), and I know how to fix that, but to be sure I flashed my old 4.4.2 ROM, just to have a known base. And spent 10 minutes here answering a few questions while it flashed. Watching Odin creep gets old fast. Not the first time - your heart will be in your mouth until the phone is working again. But after flashing a few ROMS, you'll probably want to flash
TWRP to make it easier to switch between them (and to keep your entire data partition - where each icon is on which homescreen, all your contacts, apps, videos, everything - with one simple swipe. I save mine about once a week, and keep about 2 older ones. And a few working systems. I don't want to use a phone without TWRP [or SafeStrap, in my case, since the vootloader is locked and I can't install TWRP directly - SS traps the boot process and runs a modified TWRP.])