What you describe is hydro-air, which is a hydronic coil in the ductwork airstream, heated by another source, usually a boiler of some type.

After that this where he gets a bit confused. You see any fired appliance with a chimney or single pipe exhaust will use ambient air for combustion and discharge exhaust. Whether the direct heat source is a direct fired furnace with a heat exchanger or an in-direct fired heat exchanger (hot water coil) either systems can dry out air or most often expel humid & conditioned air from the home causing infiltration that brings in outside cold, dry air to replace it. Both systems can reduce this from happening by using a sealed combustion setup that draws in combustion air through a pipe and expels it with the by-products of combustion.

Usually the complaint with forced air is drafts. Although a furnace may flash off a bit of humidity in the air, passing over it, on a 2-pipe sealed combustion system, the humidity is still there to be reabsorbed in the conditioned space. The bad rap of scorched air came from old drafty chimneys & single pipe systems.

So you see the air while warm, it is usually the draft which results in additional evaporation of our skin that causes people to believe it is dry. With radiators, baseboard and wall or floor radiant, the air movement is minimal, thus tends to be more comfortable at lower temps.

In conclusion, having a hydro-air air handler which can be for AC and has a hot water coil for heating would be very much like a furnace. Hydro air units are usually used when a home has significant other type of heat such as radiant or whatever and the hydro air is used either as a supplement or conditioning a space without any heat after a remodel such as a basement game room where there was no heat installed using the existing boiler.

Thanks.
Is sealed combustion a standard setup or is that something the installer may or may not know anything about?

Fairly standard with 90%+ efficiency units (gas boilers and gas furnaces), especially with variable speed furnace units or modulating condensing boiler units. Although some cut corners or are cheap and don't run the second pipe.