Do polyfluorosulfuric acids like H2SO2F4 exist?
As the comments imply, no dice.  You can, of course, make a six-coordinate sulfur compound with the formula $\ce{SF6}$.  But trying it with a mixture of oxide, hydroxide and fluoride ligands instead of just fluoride presents the opportunity to evolve $\ce{HF}$ leaving the sulfur with a lower coordination number.  There is a five-coordinate compound $\ce{SOF4}$, but otherwise you should expect the sulfur to get down to four-coordination.  So the only stable protic acids you can get with one sulfur atom and oxide, hydroxide and fluoride ligands are plain old $\ce{H2SO4}$ and the more strongly acidic $\ce{HSO3F}$.