I don't have much experience with fitting tires, so they may physically fit, however you probably wouldn't want that setup. I believe the MX-5 Cup cars (NC) ran a 225 tire on the stock 17x7s, and that's probably the upper limit. When you have that wide a tire on that narrow a wheel, the turn in crispness will be crap. I think for 235 you'd want to go at least a 17x8, if not 9. Just my .2 cents.
2006 MX-5, marble white with black OEM hardtop: Flyin' Miata Stage 2 suspension, Flyin' Miata exhaust, GWR Helmholtz mid-pipe, Hard Dog M3 roll bar, Hawk HP+ pads, stainless steel lines, GWR/Moroso aluminum coolant overflow tank, Voodoo shift knob.