Depends on the bank. Some will let you recon immediately because they have access to that info, or they'll HP you again on the spot so they don't care about the reasons for denial. Others will require you to wait for the letter. Then there are banks like cap1 and discover that are pretty much automated and you can't recon at all.
Who'd you get denied by?
You should still use your Tires Plus card here and there even if it's 5 dollars (well depending on Limit) to keep it active and so you also don't risk a CLD but that is odd I would say call immediately but I don't bank with PNC but if I had a small CL (for example with my HD card) I called right away and they raised my limit and I know some places will actually tell you just wait for your letter but you can always call right away and ask if they say you can go ahead and recon then you can shoot your best shot but if they say it's out of their hands and to wait on mail then wait 6 months minimum and try again. :/ It's hard to say without knowing exactly why they said no go
Were the CO's still reporting a balance? If they were PIF and 0 balance that might have looked better. If they show a balance that goes against your aggregate util and you lose points depending on the %.
The best advise is take care of the past so the future will be easier to get what you want. Set up payment plans to pay off those CO's so they quit reporting. Settled or paid is a whole lot better than owed. Once thats done and your score rebounds some. Then maybe you'd have a better chance. Some banks see you have charge offs and wonder if you get sued can they still pay us at the same time. Make sense?