It could conceivably be absorbed by the Cheato if your cheato is healthy and is at the right size to absorb whichever excess nutrients you are putting back into the water. Theres not a calculation out there that I know of to be able to figure that one out though. I don't think the bioblocks will be able to help all that much either, you're limited by your current bacterial population and these usually self regulate to your current levels. So extra won't be consumed for some time until the populations catch up.
I love the no water change concept, and it does work. But in this case I don't think that you should look at a WC as an easy escape or a continuous chore. Look at is as a tool in your belt. Really you would be only looking at 1-3 water changes and that's it. Then it's back to no water changes atall and you can continue on learning and growing as a reefer.
FWIW, water changes are a VERY natural way of combating issues, certainly moreso than the original Hydrogen peroxide route you were planning on taking. All our natural reefs go through a constant WC 24/7 as currents wash over them with fresh water from other areas of the ocean. This takes waste away and replaces it with fresh elements constantly which is what stability is all about
Not trying to poke holes in your reefing philosophy here, but maybe just trying to show you a different side to things
I do think your best bet is to try and beef up the CUC with some known GHA eaters like turbo snails if you truly want to go the natural route and sit back and wait for them to do there thing.