You don't "need" a new tune. In fact, I didn't have the tune changed at all when the converter first went in, and my 60', 330' and 1/8 mile ET's all dropped by 3 tenths of a second while my 1/4 ET dropped by 2 tenths.
However, there are benefits to tuning for a converter. The factory only locks up the converter in 4th and 5th gears. I later had my 3rd gear programmed to lock up, as well. I also have the lock up happen much sooner at wide open throttle (1/2 second after each upshift) to pull even harder on the tall end of the dragstrip for higher trap speeds. For example, most supercharged Mustangs with the same horsepower as mine tend to trap in the 107-109 mph range, but mine traps in the 110-112 mph range.