I have a Galaxy S4 T-Mobile edition. (M919) and it is unlocked. So I know I should be able to put in an AT&T sim card and it will work.
Is it possible to flash an AT&T rom (or one of those multi carrier rom's) onto that phone and have it work?
Yes, it is possible for most, but only custom cwm flashable packages, and, as long as you flash a kernel for the tmobile s4 after flashing the rom. The ROM does not have to be specifically written to be used on at&t and tmo.
AT&T and Tmo phones are identical except for the modem bands, bootloader and some other minor kernel parameters. The first two are never included in cwm packages, and the second can be mitigated by using a kernel for the variant.
Most custom ROMs (CMW/TWRP packages) are interchangeable among almost all the variants of the s4 including at&t, tmo, sprint, i9505, i9505g, (not i9500 and i9506) as long as the ROMs are not completely dependent on a single version of a custom kernel.
In other words, if the ROM does not specifically require a custom kernel by the creator and can run on any other made by someone else, then you can run that ROM on the variants as long as you flash a kernel specific to the model. For example, on a TMO S4, you can flash a i9505 custom ROM and consecutively flash a Tmo kernel for it to work (like ktweaker for instance).
Now, stock ROMs directly from samsung are different, because they are complete packages, they include too many partitions that can't be flashed. For example, the modem image, it can't be flashed across variants because they have different modems. Another example, the bootloader, variants have different bootloaders, some locked, some unlocked. Thus, only custom cwm ROMs can be flashed because they do not include any of the above, only system, data (sometimes) and kernel. However, you could extract the system image from the tar package and flash it directly, without flashing anything else.
Which is why, I don't recommend you flash an AT&T rom. Instead, get a custom one.
