Sylph.Royalblood said:
do u get more Hq with advance cooking support or does it not help
"Synthesis image support temporarily raises your skill by 1 point. Advanced support raises your skill by 3 points, and requires a small fee based on your crafting rank."
~ taken from
This cooking site
It can raise you enough skill points to put you into a higher tier, if your cooking skill is on the edge of the next tier. :)