You can provide a redirect URI as an argument to the oauth authorize call and it will use whatever you provide. Once you have a valid token the API calls don't have any check on the domain so you can run code from localhost or your server.
The only other restriction with localhost is that you won't get any webhook calls. You will need to use cURL or some equivalent to generate webhook calls targeting your localhost environment.
Edit: It's also possible that there's a special case for the redirect_uri being localhost. Either way, I test on localhost all the time without a problem and without needing to change the registered callback URL registered with Strava.
