/edit, it's not as bad as I initially thought, at least not the best-case scenario.
I.e.
Turn 1 - Buy chapel
Turn 2 - Buy warehouse, reshuffle
Turn 3 - Draw Ch, W, CCC. Play W, draw EEE, discard CCC. Chapel EEE. Draw CCCC (reshuffle), plus 1 more. Deck is 9 cards, draw pile is 4 cards.
Turn 4 - $5 (if you get a copper). If you get chapel or warehouse here, it's awkward. You won't warehouse. You'll have to chapel a single copper. Lets assume best-case, and you draw a copper. You buy a $5 here.
Turn 5 - Draw W, CH, C, C, reshuffle, plus one. Deck is 10 cards, draw pile is 5 cards. If you warehouse now, you will either chapel 3 coppers, 2 coppers (if you draw CC plus your $5 card), or have CCC$5 card hand. Chapeling 3 coppers is decent here, if your $5 is a "silver" such as montebank. Chappeling 2 coppers is worst-case scenario (you'd likely discard the chapel if you draw your $5, as CCC$5 is pretty good).
If we are looking at best-case, you are warehousing to a montebankCCC hand, and are doing pretty well, considering a 4/3 start. You are in a position to montebank him most of the next turns.
So best case scenario, this opening doesn't look too bad.
Worst-case scenario would obviously be W/Ch as the 11th/12th cards, shuffling into CCC for your hand, and warehousing into CCC. That's a complete disaster, but any chapel hand can do that.
Looking at a middle of the road example, warehouse would give you a higher probability of trashing estates on this and potentially your next chapel turn. After that, it's not dead, since it can cycle the now-dead chapel.
If it doesn't beat Chapel/Silver, my gut is that it's at least close. And I would say it's ahead if there's a powerful $4 or $5 (especially a +$ attack such as Militia/Montebank, where not having that silver in your deck is actually a good thing).
I can also see this as being good in a quick bishop rush, where the main goal is to trash down to a Bishop/Silver/Silver/Gold/Province deck as fast as possible. Getting a tight deck quickly is critical, and it doesn't need a whole lot of buying power. It only needs Silver/Silver/Copper/Bishop so that it gets the gold, then it's off to the races.