It has been extensively studied (it's been around for 36 years), and there's no reason to believe anything will happen to you whatsoever. Keep in mind that you only eat one six hundredth as much as you would sugar.
Conversely, imagine if sugar were a newly discovered sweetening compound, seeking FDA approval. They wouldn't get past one safety trial before "serious concerns about long term effects" knocked it out of the running.
Analyzing the relative risks of sugar and sucralose, there is just no case to be made for sugar being the safer bet.
That's pointless speculation, and you can play that game all day until you're arguing that nothing is safe. How can we really be sure, after all, that trace compounds from sea salt aren't causing slight DNA damage that will turn our descendants 150 generations down the line into eight-legged mutants?
The fact is that there is no more reason to believe that sucralose will have some as yet unobserved negative health effect than there is to believe that it will have some as yet unobserved health benefit.