It can, depending on the accent used, but even then would be considered assonance which is defined as resemblance in sound or a partial rhyme.
once once once
Them again
that again
Yes, if you pronounce "again" to rhyme with "gain".
Hannigan Flannigan can again fan again
once
Ten
give me a peng
no.. not really
The word "what" in that sentence ("I can't what to play") makes no sense. Perhaps you mean "wait"? Please see the related question below for "What rhymes with again?"
abstain stain again
Again, fin, tin