No you won't burn the converter up. You'll be fine driving it around.
The worse thing that will happen is you might end up in limp mode if the computer thinks your trans is slipping from the stall. The computer calls it a "non shift". When it commands a shift it looks for rpm drop. If it doesn't happen enough to satisfy the computer it may throw an SES light and possibly disable some functions of the trans like converter lock up. This is easily reset by turning the key off. Or You can tune this function out.
But that usually won't happen with anything under 3,500 stall. There are plenty of people that run a 3,000 stall with no tune.
Besides turning that limp mode feature off, the only thing a tuning for a converter does is dial in the shift point and times.
So i'd say, let er rip tater chip
2006 GTO M6
Motor - Stock with Vararam
Bunch of suspension
Bunch of brakes
12.81 @ 110.6 2.03 60'