Help!! How long will hair algae survive on dried rock?

I would do a good reset of the live rock. Cure/cook/acid bath, whatever method you use. End goal is to make sure all the nasties are off the rock as well as get any excess nitrates and phosphates leached out.
Any dead matter still on the rock will break down and feed algae. Any nitrate and phosphates locked up in the rock will again fuel future algae issues.

 

Dry matter is typically dead, but depending on the location and conditions, it might not actually be 100% dried out, like deep in the rock. But that is probably not a concern. The concern is really 2 things:

1) stuff that is on the surface and rather "soluble" - this is your dried up hair algae, etc. Usually you can get rid of this by powerwashing, and you'd be surprised how much comes off, so at a minimum, I'd do this

2) stuff that is bonded to the rock but can still "release" - this is typically what leads to the "dry rock" growing GHA like wildfire after a few months. Sometimes, that is ust the way it is, your tank will go through a series of changes over the first 6-12 months and algae is one of those stages.

Go to #15 here - Mything the Point, Part Three: Conclusion - Reefkeeping.com

The other is when calcium bonds with phosphate on the surface of the rock. This could/would have happened in the previous tank setup under the right conditions. It crystallizes on the rock and you can only remove it by lowering the pH below 7.0, so this is the problem people are trying to solve with their "phosphate laden rock" by treating it to an acid bath with Muriatic Acid (hydrochloric acid) for a short time. The other way is that some bacteria in the tank can release the phosphate by a process called "cleaving" but this takes a while and usually means you're dealing with algae for months or even a year or longer.

"cooking" the rock (more accurately, "curing" it) is really the right thing to do no matter what, powerwash it. Acid bath is optional but might be helpful, it's just not very fun to do and you have to read up as you are dealing with very strong acid and fumes so you have to understand the process (and what not to do).

Acid will dissolve your rock until there is no rock remaining, so it's something you to just to remove what has built up then you stop the process by neutralizing the acid, something like that. Also it's not 100% guaranteed to solve a phosphate-laden-rock problem, but it's not going to make it worse (I don't think)