If a fish consumes prey that is too large to be completely swallowed, one of a few things usually happens:
1) The fish will spit the prey back out again after a while.
2) The fish will slowly digest the prey- and this may take several days to happen
3) The fish may be so engorged that is dies simply from the energy cost, trauma, etc. associated with the hunt. (This happened very recently with a largemouth bass of mine that, after 2 years in my care, ate 14 fathead minnows one day and was dead the next.)
In any case, fish of the order Labridae (of which all cichlids, such as angelfish, are) have throat teeth designed to, among other things, keep prey from escaping once in the throat. Although you probably couldnt harm the fish by pulling on it, you will likely not get the fish out.
The real danger here is the decreased water flow over the gills. Because fish do not respire through the throat, they cannot choke; however, they can suffocate if the fish blocks all of the water flow, and the fish goes long enough without closing its mouth (which it must do to pump water through).