He might. If Barnes came, I agree he would take all or nearly all of the minutes used by Semi, Grant, and Javonte, plus maybe a couple minutes from current backcourt. But mostly I think the team would play fewer two-big sets - instead of 60-70 minutes going to Theis-RW-TT it might be closer to 50. So a lot of his minutes would come from the bigs. Theis could slide back from the 4 to the 5, e.g.
If they bring him on, it would be ideal to move one of the current bigs.
You just did a good job explaining why I am not that excited about Harrison Barnes. He is less PF than Marcus Morris was for example but you are saying that we would need to play him mostly as a PF (or force us to play without a PF). Marcus Morris and Horford worked pretty well as a "big" pair but that type of line up can't be used all the time, there just isn't enough size. Barnes and Theis or Barnes and Thompson can't even equal Morris and Horford but that is what we would be faced with needing to use.
You are comparing Barnes and Theis to Morris and Horford, and saying that Barnes and Theis aren't big enough to be used as a primary lineup.
If you are playing a team that is much bigger, it isn't whether you can match up, its whether you can win the mismatches. Theis and Barnes are better suited to winning the mismatches than Morris and Horford, because they are both quicker and even more switchable.
Of course , the biggest players, especially Embiid, will push them around, but the bet is that he won't be able to handle the team quickness and that the C's will be more successful at digging down on him in the post. Barnes and Theis should be more able to run bigs off the court.
When you start from a base of Tatum and Brown, that strategy of switchable defenders is your best option, unless some monster big falls into your lap.