I have a TS CTA staff. Do I need to invest 1 hard point for thunderstorm to hit or can the staff's +2 to TS allow me to use it without having to invest in a point?

yeah afaik it won't trigger without a hard point

you need at least +1 TS on your main side, either from another item or as hard point

If you are using that staff on a sorc, you dont need to have any hard points into thunderstorm.
Any other char wont be able to use thunderstorm.

you can cast it on CtA slot without hard points, but the effect wont trigger when you switch to your main weapon slot and dont have any TS bonus there