NO it would not make sense. ssgss is not a power level because it has no multiplier. IT gives goku complete control of his ki. So it would make no sense to give him ssgss ssj3 when it will all still be the same except a different look. People ask can goku as a ssgss kill andriod 17. YES he can the reason he did it was so he didnt kill android 17 or weaken him before the tournament of power because goku controls his ki.
He has the option (SSJ Official Multipliers)
SSJ x50 Base
SSJ2 x2 SSJ x100 base
SSJ3 x4 SSJ2 x8 SSJ x400 Base
(My multipliers for God ki)
God Ki x800 Base
God Ki SSJ x40000 Base
SSG(beginner god ki) x320000 base
God Ki SSJ2 x80000 Bas3
God Ki SSJ3 x 320000 Base
(Mastered) SSG x72 million
SSB x360 million
SSB2 x720 million
SSB3 x5.76 billion
SSBKX10 3.6billion
SSBKX20 7.2 billion
SSJ3 will just drain Goku energy more than Kaioken so kaioken is a more powerful and less draining option even being in SSB puts a strain on Goku's Body so he has the option to, but no,