If your clients trust the self-signed certificates (by updating their certificate stores, adding up a self-signed root CA), then, as of today, as far as I'm aware there won't be any warnings. No guarantees that this situation won't change further down the road.
I doubt there'll be any warnings. Otherwise Chrome wouldn't work in company networks. If you have domains that are just available internally (not even on public DNS), self signing is the logical solution. Still provides you with the advantages of encryption.