I doubt the Source engine uses multiple cores at all, and HT offers little or no improvement. The Source engine debuted in 2004 but the first mainstream dual core desktop processors weren't released until the following year (at least, from what I remember).
HT was first announced in 2002, so Valve may have built it into the Source engine, but I doubt it offered any meaningful improvement. I remember playing Half-Life 2 on a non-HT P4 and it ran perfectly.
The Source engine is well-known for being light on its feet, it doesn't need a massive amount of computing power, so it's understandable that Valve wouldn't waste time developing it to support a new technology like HT.