"Níl aon rogha agam."
Translation:I have no choice.
To me the aon gives some definitiveness to the lack of the thing. Níl hata agam is a kind of an uninteresting fact whereas níl aon hata agam suggests that I've looked and can't find a single one of the dang things. You'll sometimes see a construction like níl hata ar bith agam to give a similar sense.
It'd be the same difference as English "I have no choice." versus "I don't have a choice". So, yes, pretty much.