FFXI Wiki Says Adv. Synth Support Doesn't...

Contribute to HQ rate. Is this true/proven?

It's only true sometimes, it depends if the 3 skill you get from advanced support changes your hq tier or not. If you're 8 skill over a synth and you get advanced support, it will increase your hq rate dramatically, since you'd be T1 at 11 over cap. If you're only 1 skill over a synth, it won't help at all, you'd still be T0

It's false and proven... Don't trust everything Wiki says. Even when it was updated regularly it wasn't totally reliable, especially on issues like this. Somebody has some 'peculiar' luck, assumes there is something else to blame and can't accept they just got lucky or unlucky... and then goes on an editing spree.

Now that it's not moderated, there's a higher chance changes like that would stay. Yes, it does contribute to HQ rate in the way Ganukay described it above. I can tell you that from personal experience, as can many other crafters.

Adv. Synth support only increases the likelihood of not breaking the synth. This holds true when your skill level is increased.