Yes, Bill, this should be no problem. First of all, I suggest using my method of auto-generating filenames for your form submissions. View that here:
InfoPath – Auto-Generating Filenames
Using this concept, you get unique filenames that the user does not type in. You may already be doing something like this. If so, then you have a field like the one in my blog: strFilename. If you have a field like this, then it is the trigger point for your data validation logic. Basically, instead of using "Cannot be blank" to make fields required, you put data validation on them that says "If strFilename is not blank and requiredfield is blank." If you have a lot of fields, this will be cumbersome, but it is very easy nonetheless.
It's not cumbersome at all if you use the Infopath 2010 client, because you can copy and paste rules. I am doing this already for all of my 2007 and 2010 forms using the Tech Preview bits.