What happens if I don't clear my installation in time, and I don't arrive to my gaining unit on the report date of my orders?

I've gotta echo SGM Erik Marquez's comment.
Get an amendment!
I had an issue a couple years ago with clearing up a medical issue (was a non-issue, but I needed to get it cleared) before I PCS'd to Turkey. When I realized I would not be able to clear my losing station, I talked with those responsible for Orders, explained the issue, then (after a couple of days) received an amendment to my orders with a week later report date.
Made everyone happy and I was able to get everything done before I departed, then arrived ready to hit the ground without anything from CONUS hanging over my head.

Sounds like you need to get with your unit leadership, and make the request to have your orders amended. You want to get this fixed BEFORE departing your current unit... I would suggest NOT showing up to your new unit already AWOL.
Even if your at fault, that is likely to be handled in a more advantageous manner at your current unit where they have some background on you, knowledge of the post clearing precess, tasking you were put on conflicting appoints you had.
Show up at your new unit 3, 4, 6, days after published report date and you get to try and convince them were not AWOL.. They don't know you, or have anything invested in you at this point.... Your a line number thats it.

As most have said, get the amendment and, if you can sweet talk someone, have them give the gaining unit a heads up call to let them know what's going on. Easier to let your old unit give the explanation before you get there than walking in the door UA in everyone's mind.