It really depends. Keep in mind the main purpose of the flexpipe- to absorb movement in the drivetrain and exhaust.
Let's say you have prothane mounts and stiff exhaust hangers, you might never run into an issue because there would be little movement in the first place.
On the other hand, let's say you have stock mounts and worn suspension hangers, eventually something is going to fail, likely a flange weld somewhere on the header or exhaust. You wouldn't do any serious damage, but you'd break something eventually.
If you're autocrossing, you're obviously driving the car hard. Suck it up and fix the flexpipe. $160 seems pretty high though. Screw that place! Here's a 2.5" flex for under $30 shipped:
http://cgi.ebay.com/ebaymotors/2-5-x...spagenameZWDVW
A good exhaust shop shouldn't charge more than $40 or $50 bucks to weld that in place (the shop I go to would probably charge me $25).