Yes, but depends.. there is normally a cut off date..

Say u see doctor on the 1st of july 2009 and your last day is 31st of July 2009...

HR cut of date for submission of all claims (in the case of my company), is on the 15th of July 2009...

A claim should be possible.

Let me clarify,

1st July see doctor
2nd July submit claim
15 July cut off date
16 July get paid for medical claim

Say:
Even if...
14th/15th July see doctor
15th July cut off
16th July get paid for medical claim

Why?
First of all because I am still a staff of the company (until such date i have been [employee/employer] terminated, I will not be entitled to the benefits), therefore i am entitled to enjoy all benefits extended to me during such time while i am still under the employment of the company.

Depend Factor:
1. Will your boss sign off your claim? If he/she doesn't sign off, than obviously is another factor to consider.

if your referring to my "possible".

than i hope you can quote my statement and explain yourself rather than a one liner.

I want to elaborate further, if it is POSSIBLE wouldn't you want to have a go at it? If you claim approve happylor, if claim not approved than too bad.. the point is at least you tried.