When a baby has gaps between teeth will the gaps stay like that?

Yes in primary teeth: The secondary dentition is quite different.

There is a purpose: These gaps or spaces are present and with facial jaw bone growth allow room for the adult teeth (which are much larger) to fit. Often, though, due to a mis-match in the size of a child's teeth and the size of their jaw, they may develop crowdiing or spacing of teeth and require orthodontic treatment. Always consult with your dentist if you have concerns and want answers to specific problems.