The one hesitation I'd have personally, as I know next to nothing about the TAM, when it comes to trying to run Linux on it is whether or not its built-in LCD requires oddball video timing, and whether there might be bad consequences should Linux fail to recognize that fact and attempt to reset the video mode to "normal" 6500-plus-a-CRT timings.
I mention this because I happen to own a Dolch PAC portable of about the same vintage as a TAM, and its built-in 800x600 LCD display is linked to a video card with a custom BIOS that "knows" that the LCD's native timing is nothing like a CRT monitor. (The 800x600 mode, for instance, uses a 40 hz refresh rate.) Debian's X.org server surprisingly enough is able to pick up on this ancient machine's peculiarities and automatically do the right thing, but if the TAM depends on some oddball hackery tacked onto the motherboard's built-in video support that Linux can't detect it's possible it'll go all pear-shaped when you boot up. It's been a good half-decade since I last ran Linux on a Mac, but I remember X support being touchy, particularly on "oddball" machines.
(The original iMacs were another good example. Monitor auto-detection didn't work, so unless you put custom modelines into your X configuration file to force it to stick to the the oddball resolution/refresh rates the built-in monitor actually supported you'd get a black screen when the ATI driver would pick a "standard" multisync rate instead.)