> But I wonder if someone with Emacs 24.5 would be able to download the
current json-mode from MELPA, i.e. whether it would be shadowed by the new
version in ELPA (that requires 25.1), or not.

It won't. When multiple versions are available from different archives,
package.el shows all of them.

Upgrading is a little annoying though. In 24.5, if you hit U in the package
menu after having installed one version, package.el will gladly try to
install any newer version available. In this case it will even try and fail
if you don't meet the 25.1 dependency.
Both issues are fixed now.