Hi Tim,
Welcome to the site. I think you'll find it to be very helpful to you and your son as he continues toward HS baseball and maybe beyond.
"Tournament Team" can mean a lot of different things at that age. Some are very local in nature, some national and everywhere in between. Some are part of organizations that field teams at various age levels along with various degrees of training while others are not much more than pick-up teams looking to play a few tournaments beyond rec ball. So, you also get a wide variety of what types of try-outs you may see.
Some will try out your wallet and see how much you can pony up. Some will be desirable programs who get great turnouts and will run various stations where your son may get a few hitting reps in the cage or on the field and some fielding reps and perhaps move on to throw a short bullpen. Some may include a simulated game where he may see a few innings and maybe a timed run. Some will just hope they can get enough kids to show up to form a team.
What do you know about this particular group or organization? If you don't know anything about them, perhaps your son knows someone on the team. He may be able to get some insight on what to expect for this particular group. In any case, at this stage, it sounds like it would be a great next step for him to play some more ball - hopefully a step up in competition.
I do suggest you prepare yourself for both scenarios. If he is asked to play, have a short list of questions for whoever is running things so you and he know what to expect and there are no surprises as he plays out the tournament schedule. You may want to ask about things like costs, playing time expectations, commitment expectations, schedule, protection of pitchers' arms, training/practice opportunities, etc. If he is not asked to play, perhaps have him prepared to ask what he needs to work on so that he is in a better position for future opportunities. He is still plenty young and most areas have programs of varying skill levels. As he continues to work on his game, he is likely to find open doors as a LHP.
Let us know how it goes and what you and your son experience with this particular group.