When you convert a webinar to on-demand, does the registration URL stay the same?

I've set up many webinars as classic ones, but on-demand will work better for us. If I convert them will:

• the URL to the registration page change?
• the registrants keep the same URL to log in? 

By the way, I already know how to convert them, so I do not need that information. I just need the answers to the questions above. Thanks!