TLDR: Practical answer: No.
Longer answer:
In theory you can. If you started something like nohup myprog &
from inside the screen then it will continue running. It will ignore a hangup signal and will not have any input, but in theorie you could continue working with it.
In practise this is not the case. Thus unless you want to attach a debugger to the running process and rewrite its file handles and make sure that the process handles -1 signals when you close screen ... then the answer is no.
If you are ready to do this, I have a bookmark at home pointing to [SU] where someone did just that. Saved for awesomeness, not because it is easy and trivial to do.