The direct answer to your initial/primary question is "yes, you can add lean at any time
Just be aware that adding lean angle (without increasing speed), will cause your line to tighten. In other words, if you are carrying a constant speed and sufficiently making it around the corner, then add more lean angle, you could run off the inside of the corner. But yes, if you are into a corner and see you are going to run wide, then you can either reduce your speed or add more lean angle.
As far as tires, that is a tough question. You will get tons of different answers, it all depends on who you talk to.
There is a HUGE variance of speed in the Intermediate group. Some guys are running almost an Adv pace, some guys are barely above a Nov pace. There can be as much as a 20 sec different in lap times in the Int group. So it is really hard to make any suggestions based upon group placement. In order to give good feedback, you would have to provide some lap times compared to race lap times at the same track.
With that being said, I know for a fact that Q3's are capable of handling a race pace. I have seen someone turn laps fast enough to win races on Q3's. The only issue is that they wont handle that pace for race distance, they will overheat.
Something else to keep in mind is that it takes a good bit of carcass stress/flex to keep heat in race Slicks. And to be honest, that means most Intermediate riders won't ride hard/fast enough to keep adequate heat in race Slicks. Which means that most Int riders will actually have MORE grip with something like a Q3.
Then of course there is the flip side, most Int riders won't be asking for ultimate performance out of a race Slick because of the reduced pace...which means they can get away without the Slicks being at optimal temps.
You might want to look at something like these. The are classified as "Track Day Slicks". They are Slicks (no grooves), so they will provide a little more grip, but they aren't a true race tire so they will heat up faster and aren't as stiff (meaning they don't have to be worked as hard to maintain heat). They are basically an "in between" tire for somebody who might be going faster than what street tires are good for, but who isn't quite ready for a full blown race Slick.
Pirelli Diablo Superbike Pro Rear Tires - Sportbike Track Gear