Well, I tried it (actually, I tried it the day after I posted this but didn’t update it)!
Here was our game:
Starting Decks: 3 Shelters, 2 Mills, 1 Poacher, 1 Village, 1 Pawn, 1 Woodcutter, and an Estate.
Kingdom: Lighthouse, Courtyard, Masquerade, Workshop, Feast, Monument, Festival, Market, Minion, Band of Misfits.
After the first two turns or so it actually felt like a relatively normal game of Dominion. The only thing was that the turns took extra time because of all the chains of cantrips. But once you got a good hand you could buy some money cards and trash your junk cards with Masquerade, so it became relatively normal after a while.
I’d do it again with two or three players … we played with five, and it took a long time between turns, so I’d advise against that. But just in case anyone is wondering: it can be done!
And it does pose an interesting challenge!