After bringing home a growler and not finishing it before it went flat, I began to wonder - could I bottle it, add some sugar, and re-carbonate it? (The beer was naturally carbonated and we'll assume it was not contaminated)
In Theory yes you can, but YMMV.
First there may not be alot of yeast left in suspension if any at all. can be fixed by adding a neutral yeast to it.
Second you have introduced oxygen to the beer, which will cause it to go stale very quickly. Cant be fixed, only drink it faster.
Third, which you mentioned is contamination. but per your comments, not a factor.