It's easy to say no but the first question to ask is why?
In snow a skinnier tire is better and the inverse is true during the summer.
I personally recommend googling Miata Tire Calculator so you can input your stock tire dimensions and play around with width and sidewall to get the least amount of difference in tire dimension.
I would also recommend looking at discounttiredirect.com and tirerack.com for good prices on tires. I'm a little leary about ebay when it comes to things like that.
Whenever a question about tires comes up I always recommend my favorite which I have since placed on every car in the family which is the Yokohama Avid H4s.

. Jon.