Rails dev here! 
To be more precise, rails console doesn't give you access to the running rails server. Rather, it gives you a REPL with some packages (gems, like ActiveRecord) imported automatically, plus a database connection, a logger, etc. Basically it bootstraps everything the server would need, but instead yields to the REPL.
I believe most of this could be accomplished by simply importing your application module and running a bootstrap function, which would no doubt depend on the framework you were using (or not using).
Swift already has a great REPL, but as far as I can remember, getting access to SPM packages from the REPL is still pretty tedious. I think it would be a huge boon for SPM to provide some conveniences around that. (This may have changed since I looked at it last) Furthermore, being able to start a REPL with a function call would 
(Ã la the Python debugger, Javascript's debugger, etc.)