It’s always wise to provide a hidey place for your bunny to have in his habitat to feel secure. I answered another of your posts just now, but my suggestion is the same: try a willow tent. It is big enough to lie under, pointed at the top to prevent climbing, edible so good for nibbling, and dark and cozy. You could also get one of the Oxbow hidey enclosed round ones with a front hole opening, which would soundproof it a bit more, but only smaller bunnies fit in those. Check out the BB store for enclosures you think he might like. Any enclosure will sound proof it.
It will bother him, but not harm him, An alarm I mean. One night in an apartment complex we had a real fire alarm, and the noise from it in the hall on the way out almost made me deaf, it was so bad. I put my bunny in his carrier and got out of there. Actually, a carrier is a very good enclosed space for him to go if you are doing a test and know ahead of time.