On a tablet, is it possible to install Linux on an SD card, and let it boot from it without the need to partition the internal memory and without touching Android?
For a native boot, out of the box, no. Android tablets generally have a locked bootloader and there would likely be driver issues. However, it has been done. For this to be done, however, you need to do quite a bit to the tablet.
I recommend you research which distribution of linux you want running on a tablet, then look for guides (such as on xda-developers.com), then buy the corresponding tablet.