Frame bracing like a roll cage and strut tower bars will help the car out with the stress, but mostly they are good so the frame will flex less and ultimately give better and more precise handling.
I don't drift, but from what I understand...the way a frame is made allows it to withstand drifting without bending in all cases but a crash, but you would risk bending the frame in any sort of mild/major crash. I can only think of one problem area and that's the roof...if you have t-tops then I wouldn't suggest drifting unless you have proper frame bracing...and even then I don't think it's the greatest idea. Moon/sunroofs aren't too bad for flexing and they don't get the cracks at the stress points like t-tops since they provide decent rigidity usually.
Convertibles are definitely not the best for drifting and handling, but you still aren't risking bending the frame though...they just flex so much more than a solid roofed car when you push them hard...but the newer mr2s can drift alright and they are all spyders...so it's all up to how well the car was engineered...