Convexing a SAK edge won't give any more support. You're removing material, not adding.
It does improve slicing ability by thinning and tapering the edge bevel.
What I've done on a couple SAKs was to lay the blade flat on a slack belt grinder until the edge bevel goes down to zero. The slack belt creates a convex primary grind, tapering down to a zero edge. No secondary bevel. After taking care of any burr, this transforms the already decent stock grind into near straight razor performance. Microbevel honing takes care of subsequent touch ups.
Convexing just the edge to perhaps 1/8" wide is easier(especially if no power tools are available), and offers near identical results, as long as it tapers down to zero. Go for eliminating the original bevel, which can be clearly seen when reflecting light. Or to be safe, take it down until the original edge bevel is thinner than a hair. Such a thin edge not only slices well, it's easy to maintain.