Is a quarterback ever an elligible receiver? Under what formation or
circumstance? Under NFL Rules? College rules?

Here is the college rule:
All offensive players are eligible except linemen and the quarterback,
who must notify the referee if they wish to become eligible and stand
at least one yard behind the line of scrimmage before the snap.

NFL rule:
The quarterback is an eligible receiver if he is at least one yard
behind the line at the snap. Eligible receivers on the offensive team
are players on either end of line (other than center, guard, or
tackle) or players at least one yard behind the line at the snap. A
T-formation quarterback is not eligible to receive a forward pass
during a play from scrimmage.
Exception: T-formation quarterback becomes eligible if pass is
previously touched by an eligible receiver.

I vaguely remember seeing the Dolphins run this play from time to time
in the early-mid '80's. I believe Duper or Clayton was throwing with
Marino receiving.