I'm pretty sure quarry/horse trader does that pretty systematically.
The thing is, once you have 2-3 HPs, they will make it increasingly likely you get the quarry/HT combo, which makes for a double HP turn.
Of course, nothing prevents your opponent from trying the same. But the point is, if he has a structural advantage in not doing so (mostly opening/first shuffle outcome), then yes.
Unless you think he should have contested the HPs instead of buying province? Even then, you could imagine my combo triggering before T8 (it had a 50% chance of happening T6 onwards...). I could have had 9 HPs by T10 (but instead went for a fairground and 8 HP). I am pretty sure the average is T9 for 8 HPs. (edit: ok, maybe I was a bit optimistic. hitting 3$ is pretty bad: examples
8@T9,
8@T11,
8+province@T13,
9@T10,
9@T11. Mind you, in my game, the vault helped me on T5, which probably lowers the average turn to T10?).
edit: quick simulations using barely modified versions of the optimized vault and HP bots.
Vault-Xroad outperforms regular Vault against a non-vault player (80-16 instread of 76-19 against BMU). Unfortunately, the simulator makes the Vault-Xroad player discard greens on other player's vaults, even if an Xroad is in hand, making a direct comparison somewhat meaningless (the numbers are 46-49 in favor of regular vault).
Now Vault-Xroad outperforms HP-HT 51-44 assuming no p1/p2 bias (but 5/2 vs 4/3). It turns into 74-20 with the p1 bias (which is ridiculously fast). I obviously did not code my fairgrounds thing... but my point is that me playing regular HP/HT was not an option... unless p1 wasted his early 8$ hands contesting HPs, in which case I don't *need* 8 HPs, as I can now race provinces and be competitive.