Will they send me home if I can't perform well during the physical training?
The short answer is maybe, but it depends on how out of shape you are. In today's army, they will beast you, but it's pretty tough to sh*tcan you off the course. They CAN make your life so miserable you will want to quit, and if you're reg, in theory they could RTU you and send you through the course again (they can in the res too, but it's quite rare these days). But in reality, they will just make life unpleasant for you.
As a side note, how did you allow yourself to get out of shape? Not a great way to show your commitment to your unit, or your professionalism. You will likely see "arrived physically unprepared" on your course report. Laziness is something your course staff will hammer you for, not to mention your fellow section members.
Fair warning.