For a single addition, the radix is irrelevant, the carry is always zero or one: (r-1) + (r-1) = 2r - 2 < 2r.
But for a single addition you will also not save any time because you still need to do the select in series. The whole point of the radix 2^51 trick is that you can defer the normalization over several additions, but in order to do that your carry needs to be more than a single bit.
For as long as radix=2, you either have a carry or you don't.