From a legal standpoint, yes, you can file without any late accounts. Ethically, are the debts truly unmanageable or just "inconvenient"? What's changed since you ran up the debts that makes them no longer affordable? I'm not trying to be judgemental, but to play devil's advocate - if you ran up these debts and discharge them in BK, how will you avoid getting into trouble again?
There are other factors - what have you run up in the last 90 days and six months? A consultation with a BK lawyer is really important to understanding all the rules and traps.
If you decide filing is the right course for you, you're correct, your post-discharge score will be better if you have no "lates" or other derogs.
