well that's the thing, its not really added, it's either replaced pixel for pixel or a weighted average... for example, if the Ha was 10 hours and the R was 5 hours and half the R pixels were replaced by Ha then I could see it as an add equaling 7.5 hours of total integration, but not 15 hours as a direct sum... get my drift?!
it all depends on the what criteria is used for the blending
>> it's either replaced pixel for pixel or a weighted average
Doesn't matter. Regular stacking will all RGB subs also averages. And with PI, you can do a weighted average depending on sub characteristics. And on hi dynamic range targets like the Orion nebula, people commonly combine a bunch of long exposure subs with short exposure subs, usually blending the two in some manner.
We combine images in all kinds of ways, whether from one type of filter or multiple types. Again, Integration time is simply the time you spent collecting photons that went into the image. The only time you don't count is for the subs you toss.
I'm not quite sure what your goal is in answering this question. The only purpose in reporting integration time is to compare results from one image to another and see what effect integration time has. But, as mentioned above, integration time cannot be taken in isolation and there are many other factors that come into that comparison.
You can't compare integration time without knowing details about all the equipment in use, including filters. If you see a total integration time that was reported for a combination of filters, then all bets are off unless you also know how much time was spent with each filter type.