No. You can pull off up to three Shinkuu Hadokens within the time limit (although I doubt you can get in 3 of any other special except Regeneration). Although it takes longer than 6 seconds to finish all the supers, you can get the last one started right before time runs out.

There's also a glitch that if you press it again right when/after the timer runs out, you'll get out one last Shinkuu Hadoken from the recently tagged in Ryu.

So from where I see it, the limit is 7 Shinkuu Hadokens in a row.