In general, when you apply carb heat you exchange the cold air from one source with the less dense warm air from another source, thus resulting in a reduction in power ( manifold pressure), This is most obvious with a fixed pitch propellor: i.e. a loss of RPM owing to the reduction of MP. The constant speed propellor will, of course, with a reduction of power then fine off maintaining the RPM.
This is the main theme applicable to the question. Bypassing the air filter, or the possible melting of carb ice are secondary to the basic question. With a constant speed prop (note the "constant speed" reference), the governor will govern the RPM to be constant when in the governing range of engine speed. So if you do anything which reduces power on the whole, the MP must reduce, as the RPM won't. The hot air produced by carb heat application reduces the intake air density, so the power must reduce a little, and the MP will reduce.
If you do the carb heat check at a lower RPM, when the prop is already on the fine pitch stops, then the RPM and MP will reduce a little together ('cause the prop can't move to be more fine to maintain the RPM). But a 470 has a lot of inertia, so watch carefully, and give it a moment, as the effect of carb heat is much less at low RPM, so you won't see it as much.
Remember that to optimize the effect (heat) of carb heat, lean the engine more once it is applied (because the application of carb heat enrichened the engine). Just make sure to enrichen the mixture again when the carb heat is selected cold again.