It was originally titled "Black Mesa: Source," but Valve contacted the team and asked them to drop "Source" so that it wouldn't be confused with an official Valve project. To my knowledge, that's the only world they've given, which sounds like an implicit "blessing" to me.

Given that this is free, community driven and effectively celebrates HL1 I don't think Valve will rain on their parade. Besides, Valve tries to support the mod community as best as they can.

If they tried to sell it for profit I'd imagine there would be some very pissed Valve lawyer breaking down doors though - because I don't think its officially & legally blessed.

When someone makes something that's marketable out of one of Valve's games, Gabe Newell normally gives them a job or a publishing deal. That's how all video game companies should operate.