Help with specifics

Since they don't mention coming to class on day 1 with your permit already procured, I'd say that there will be structured classwork teaching this curriculum and preparing students for the permit.
It's not difficult.
But, a phone call to find out for certain would be a wisely spent three minutes so that you're not burned when you arrive.
As far as applying NOW, I'd venture that most companies would say "give us a call once you're firmly into the process" of your training.
The academies almost ALWAYS have job leads that will come and beat their chests for you and promise you the moon and back.
Since you said you're writing the check, (that's fabulous!!) you control this situation much more than 98% of students.
Most go as "scholarship" and owe their souls to their free training providers for X amount of time after graduation to repay the investment.
Now, YOU hold all the cards.

The community college does provide the testing vehicles.. that's built into your tuition. But, ASK AGAIN.
If it's not, find out early.

As far as when you do hire in somewhere and are being trained OTR, that can vary.
Some people can't drive their own passenger vehicles well and think they could drive a truck.
Some drive OK, and it just takes awhile to get the white knuckle out of them. Out here, YOU HAVE TO BE RELAXED.
Some take to it like they were meant for it.
Still... there are things a GOOD trainer must slowly prep you for. You cant possibly see all scenarios in 4-6 weeks... but if you're REALLY a quick wit, you could be ready to go it alone in 2mo or so. Don't rush it.

The pay while training will likely be at a reduced rate while you are being overseen, particularly in the very beginning when your trainer must be UP and in the passenger seat AT ALL TIMES when you are driving.
After a certain period, he/she has the option to make it a true team training venture and can leave you alone to drive while they rest. This will take a while. You wouldn't go to sleep with Stevie Wonder driving you across the country... he's not going to either.

Soak it all up. Now is when you LEARN some stuff... but it's just basics.
When you get out HERE... that's when the real learning begins.

Best of luck to you.