I believe Diesel has been on stable for a long time now, so for this use case I don't think anyone will need to worry about using the nightly releases.
Rustup makes having nightly and stable in the same machine painless, and I got in the habit of running cargo +stable build and cargo +nightly test. BTW, you don't have to do this, it just makes my experience a bit nicer.
However thus far we have never had to push a release due to a bug found in nightly. We also have never had a build break because of nightly, or even upgrading.
The only breakage i'm aware of was, oddly, a semi-recent Rustup change. Our CI was not pinning the Rustup version, and the argument defaults changed so the downloaded Rustup did not have the components needed for our CI setup.
We will however migrate to stable once Rocket becomes stable. Thus far however, we've not had any trouble on nightly. I can only assume this is a result of the Rust teams excellent QA/tests/care/etc, combined with the language itself being very easy to write error-free code.
So far we've seen about 2/3 of nights fail for our code. The failure is totally obvious. So we revert to the previous night that we know works.
Also, for the love all that is holy do not publish a crate relying on that flag to enable the nightly features, it breaks the languages stability assurances and by extension the ecosystem.