You can autocross on any tire you want.
The difference in a v12 vs a Hankook RS3 or BFG Rival (200tw tires) is huge. You'll be 1-3 seconds faster on them.
If you want to have fun, drive on whatever you have. If you want to be the fastest you can be in your car, tires are everything.
I did my first season (last half of 2013) on Sumitomo HTRZ3 (competitor to the Hankook v12) and had good results. Once I felt the tires were limiting me, I made the jump to a 200tw tire.
Bring it out as is a few events and take notes, have people ride along and/or drive your car and you'll have plenty to work on between the ears.