I know this is kind of a weird question, but I find tri shorts to be very uncomfortable as a man and thus always wear my nike compression shorts under them. Between both products, that solution isn't all that comfortable either. Are tri shorts supposed to be worn on their own? They don't really feel like it...
The short answer is no, go commando. The same goes for bike shorts, and I've had to retire some from normal use because they were getting a little thin. Of course, if you really want to wear something it's entirely up to you. I know women who wear a thong. I passed on that idea but again, it's up to you.
The idea is the pad is supposed to be just enough to make the bike seat bearable but not be so bulky as to interfere on the run which bike shorts will do with their thicker pad. You'll have to harden up in a few tender spots to do long courses but that's how the power bar crumbles.
Tri shorts and bike shorts are made to be worn without anything between them and you. This means there are no seams in places that would rub you the wrong way, particularly while on the bike. You may want to use chamois cream for a bit more comfort. If it is a, uh, visual discomfort, on the swim and bike it isn't really a problem and on the run just slip on a pair of shorts over the tri-shorts in T2.