My view on this is as follows, a rabbit hutch is for a rabbit and not a pigeon, the birds need space to fly and strech there wings etc.
You can get an old 8x6 shed from the local paper for next to nothing, rabbit hutches are to small for rabbits and i dont like the thought of keeping birds in this way.
People do keep pigeons like this but its not ideal
its nice to hear that someone is setting up so well done, but i must say try to put that little extra in an it is well worth it.
I bet you would end up getting a bigger pigeon coupe in a few mounths anyway so why not give your self a better start
all the best and good luck
this is just my opinion and people my not have the same view