Do chains on single-speed last longer than those on geared bikes?
Single speed last longer and cost less.  More metal and less (no) flex.

SS comes in 1/8 and 3/32. 
I would contend a SS 3/32 of the same basic construction is stronger than a 3/32 7 speed because it does not need to be built to flex and it is not flexed. 

I am not finding any pictures of 3/32 SS chains and the chain on my SS bike is 1/8.
So I guess it is not really a straight comparison.
But a SS will take a 1/8 and geared will not so it is a fair comparison.  

Also SS is built to take the abuse of a fixie.  In a fixie the chain has to take the braking force and gets hammered.  Note the question is SS not fixie.