Unlike Gmail and other google properties, I can leave it open for weeks and forget it's there. It doesn't affect overall system performance—because it's not demanding CPU time and forcing context switches when it's not doing anything.
[EDIT] incidentally, has Thunderbird bloated a ton or something? I used to use it on machines with 256MB of memory total and it was not the only thing I had open, and it was totally fine. And yes, HTML email existed then. I was under the impression it was—thanks to neglect, basically—still on good, old tech and the plan to "improve" it to ditch that for bloated modern junk was still on the drawing board.