First, yes, you can use the spa as an arriving F passenger. Actually, you can even use the spa (more limited services) as a C passenger. If you go via BKK, arriving in F you'll be met at the plane, just have them take you to the spa... and your arriving F boarding pass stub should suffice to get you the F treatments.
But then of course you're continuing on in TG C.
So really you're back to 'should I go for SQ F or TG F?'...
And I would go for SQ F, even if that didn't have the added benefit of a non-stop. SQ F also means a longer F flight! The only thing you lose is TG's ground service which - while nice - doesn't make up for the fact that SQ F is such a meaningfully better product in the sky. ^