All the tests should run from the standard test runner tool (currently regrtest), with the GUI tests guarded by the GUI resource, which is how it works for TK.  I always run the test suite with -uall before non-trivial commits, so I do in fact run the TK gui tests on a regular basis.  I would do the same with idle.  I hope there are at least a few other developers that run with -uall on a regular basis :)

Whether or not there is value in a separate runner is a separate question.  If there is value in having one to you and the other people working on idle, then make one.  But for those of us who touch it only occasionally, the separate runner is not likely to get used.  I wasn't even aware there was one for tkinter.

There was a push a while back suggesting that best practice would be to have all tests be in the 'test' subdirectory.  I moved email/test into test/test_email, and I prefer having it there.  On the other hand, Michael prefers having unittest/test, and has kept the unittest unit tests there.  So that part is up to you, but I encourage you to consider putting them in the test subdirectory, and if you want to do that I would help out with moving the existing tkinter tests to the 'test' dir.

And yes, either way the tests should test for the presence of idle and skip if idle is not available.