Even though that would probably work, the benefit is low and you'd have to convince the inspector that the risk of steam explosion is sufficiently low.
A HilKoil isn't exactly a code-approved plumbing device in MA even for hydronic heating, would violate the warranty of the woodstove...
...but could work if you engineered-up the necessary controls, heat exchangers & pumps.
For the amount of money you'd spend on a hack of dubious benefit you can probably install a heat pump water heater (the GE Geosprings are about a grand at box stores, and subisidized in some utility areas if you're already heating hot water with electricity) which would pull over half it's heat from the room. If that room is heated by the woodstove, over half the hot water heat is from the woodstove, the rest is from the electricity used by the compressor. In summer it would serve to dehumidify the basement too. It's still drawing heat from the woodstove, just in a less direct (but fire-safe and code-compliant) manner.
If the hydronic boiler is propane fired even a standard electric tank would cost less to operate at recent years' propane prices. If oil it's comparable in cost. But a heat pump water heater's operating cost is less than half that of a standard electric tank during summer, and during heating season when drawing heat from the room (a bit more than half the total heat going into the water), the cost of the wood-heat fraction is dependent on your cordwood cost & wood stove efficiency.
BTW: If the basement foundation walls aren't insulated you're going to burn a LOT of wood trying to keep the first floor warm mid-winter. the above grade portion of the foundation wall loses about 10x as much heat per square foot as insulated 2x4 framed walls, and if you have to keep the basement at 80F to keep the first floor at 65-70F it's even lossier due to the higher difference in indoor/outdoor temps. Wood stoves and other point-source heat sources (eg: mini-split heat pumps) work a lot better with higher net-efficiency if located in the space you're trying to heat. In most of MA heating with a better-grade mini-split is cheaper than heating with purchased cord wood in a 75% efficiency stove. If the idea of the woodstove is to cut down on oil or propane heating operating costs, it's worth considering.