Are you talking about the accuracy of your spedometer? if so yes. But not just the rim size, the overall diamiter of the entire wheel. You can get smaller rims and then put tires with a larger sidewall on them and barely effect the spedometer accuracy. But say you go to a smaller wheel and a lower profile tire (or larger, either way makes a difference) and yes.
Put both of your tire sizes in this calculator to find out
http://www.miata.net/garage/tirecalc.html