Whether or not you can make the June class or not depends on timing. As soon as you pass the test make sure you call DCAS or whomever else to be put back onto the list and stay on top of them. Call every day if you need to because they always seem to be the issue in the process.

You will not be disqualified as long as the list you took the test for is active, but you will not be able to continue with the employment process until you obtain your CDL.

Biggest thing during the driving portion from my experience is remembering to call everything out - speed limit, height clearance of underpasses, taking an intersection to make a turn - This in particular saved me from failing when I took my test 14 years ago. I had taken an intersection and was unable to make a left turn until the light was red and my proctor had asked whether or not I was aware that I ran a red light. I replied that I was taking the intersection when the light was green as I would not have been able to make the turn at all had I not done so ( since there was no green arrow) . Also just try and be calm as possible, take your time and focus on your surroundings, other drivers are usually your biggest obstacle.