I don't think anyone could tell you if the tires will be ok without being able to see them in person.

Its really going to depend on the rider more then anything. Can you tell what a set of tires feel like when they start to fall off? Are you going to be pushing it near 100% or just "feeling out" the bike? I know, personally, I can ride very shagged tires. I just have to adapt my riding to match the rubber I'm on. Brand new tires can be pushed very hard in race pace. As they get older, they will slide around more. If you are comfortable with the bike and know how it feels, you should be fine. I have ridden tires until the indicators completely disappear. I've also crashed on freshies.

Another thing to consider aside from heat cycles would be how old the tires actually are. They could have one sprint race on them, but if that sprint race was from 2006 its going go be a huge difference then one sprint race from last season.