It does not. Source: have a dock. Latest firmware installed from deck. And because the current Steam controller is a recent release, I had to try a whole mess of third party controllers before settling on PS5 controllers because everything else I tried had Bluetooth pairing issues / disconnects as you approached four controllers.
SteamDeck as a handheld is great plus or minus a few nits baked onto the power / battery life choices Valve made. SteamDeck -> TV and SteamDeck -> USB-C KVM are both workable, with caveats. I had hoped we would see the bug fixes you describe before the Steam Machine release. Alas, no.