Do puzzles make children smarter?

The main thing is that she is enjoying the activity. The added benefitsare that she is developing her fine motor skills, her visual skills and spatial awareness by doing these puzzles - all of which are good things. Its even better if she talks about how/where she is placing the pieces and can describe what's happening in the picture . If she's able to use scissors safely you could help her make her own puzzles by sticking pictures on card and cutting them up so she can find more 'stories' as she puts them together. Kindergarten teachers lives are made easier if the children are able to do up their own coats/shoes - it saves valuable teaching time.

I am no expert on how the brain works but I would say that any activity that makes a child use reasoning and logic type skills would probably benefit them greatly.
My niece has a very high IQ and could read at 3 and my sister gave her all sorts of puzzles and games to play with when she was younger. As long as the child enjoys the activity there can certainly be no harm done