Oh, heck yes it will! My AT&T 6300 is running Windows 1.03. That is the earliest Windows it can run, because Windows 1.0 was incompatable with it. I have heard it can run all the way up to Windows 3.0, but personally wouldn't take it above Windows 2.xx. Here is the specs of my machine:
*=see foot note
2 floppy disk drives(5.25)
1 30(maybe 40)MB hard drive
*I thought the AT&T 6300 came with an AMD processor. All my others have one, but this one, from the original 1984 structure(RAM was upgraded) has a NEC processor. No indications of it being a V30 or anything. The original owner left no records indicating its replacement, which leads me to believe it is an original. There are records for EVERYTHING else about the system, even the loan he took out for it....
So there shouldn't be a problem on the 1000TL. My IBM at 4.77MHz even runs it fine. Just make sure you have DOS 3.0 or higher, for maximum performance.
Most all 8088's will run Windows 3.0 (which IMO is the only version of Windows worth running on an 8088.) Even an IBM 5150 with a hard drive will run Win 3.0, although it's terribly slow at 4.77 mhz.
It's still slow (but tolerable) at 8 or 10mhz., which is an advantage if you're running a clone board and not the IBM 5150/5160.
The Tandy 1000TL is one of those interesting hybrids with a 286 CPU but only 8 bit expansion lots, right? I've had PC clone type motherboards like that (not Tandy) which ran Win 3.0 just fine, but in real mode only.
Your 286 CPU will help with the speed, which will probably be 5x or more the speed of the 8088 4.77 mhz. CPU.
You can even run Word for Windows 1x or Excel 2x under Windows 3.0 on an 8088. In that case it helps to have an expanded memory card, as 640K of RAM runs out pretty quickly on an 8088, and Windows 3.0 in real mode can't use a swap file. Hopefully, your 2 meg. card can do expanded memory in EMS 3.2 or 4.0 spec. which Windows 3.0 can use even in real mode.
You should be able to run Windows 1x OK as well. However, there is basically no software that will run under Windows 1x except what comes with it (windows write, calculator, etc.) Besides, its ugly to look at and the color 'scheme' is downright painful.