A solution that is inefficient two week a year but efficient the rest can still be cheaper than some hybrid setup.
If it is expected it simply won't work a few weeks a year, sure, that's clearly not effective.
To know whether a heat pump (air-to-water) can replace that boiler effectively and maintain comfort, I had to find out whether the house would be comfortable with water temps of 135°F or so. Is there an amount of “that’s just looking at the building construction” to make that analysis? I think maybe technically yes, but practically no.
As it was, to get an answer, I abused my old boiler by turning the water temps down (causing condensation and slow damage [planning to replace it anyway]) and seeing what happened on cold days.
I am not familiar with the nuances, but this appears to be an equation with two variables - water temperature and radiator surface area. Maximising surface area should slow you to use lower water temperature. And the lower the water temperature, the more efficient the heat pump will be?
As a homeowner who bought a 1920s house because I like the character of a 1920s house, would I like to do that? Absolutely not!
Then, because the answer is almost always going to be "yeah, it's going to be really close...", I felt well-advised to prove it via experimentation rather than commit to changing the heating plant to a system that could not provide 150°F flow temperature.
Alternately, to get a realistic measure, you'll need to set your boundary conditions about what the heat flow out of the room will be, which is a bit simpler to setup with U-values, area, delta-T, and heat capacity of materials. You'll also need to do this to every other room in the building simultaneously. This is a Manual J, or heat balance method or the radiant time series method load calculation that will balance out with the amount of heat leaving your radiator without knowing its specific shape.
If your heater can go low (mine bottoms out at 50 unfortunately), by far the easiest is to just test.
A two-part answer:
From the Mechanical Engineering/Thermodynamic angle:
> Ultimately, I proved to myself that a heat pump could work down to an outside air temp of about 18°F [which is slightly above our 99th percentile design temp] with flow temps of 135°F, so an air source heat pump could work with slightly reduced comfort on about 2% of days or could work all the time with supplementation with a 9kW [30K BTU/hr] electric boiler.
From the commercial angle:
> What killed the project is no heat pump installer was interested in doing the work (as reflected by outright declining to bid, while bidding a 4-hour gas boiler swap, or by bidding so high that they might as well not have bid, while also cheerfully bidding a 4-hour gas boiler swap). So my house still burns gas for heat.
On the engineering front: I think the answer is often going to "<hissing inhale> It's going to be close; we should probably test it..."
Calculating the heat loss of a house is really not trivial. Often you'll have no idea of the materials used or the quality of installation, and not really a way of finding out unless your up for some destructive investigation.