I bought new 18" rims to replace my stock 17" rims, but I did not replace the spare tire. I was thinking it would be ok to use the original spare, but maybe I am wrong about this.

What are your opinions about this, could I do damage using the 17" spare? just to get me home?

As long as the outer diameter of the spare is close to your current wheels, you'll be fine. Use the link below:

http://www.miata.net/garage/tirecalc.html

an inch one be too bad for a spare