…finally pointing domain at new site

Okay – so I am ready to point “mydomain.com” at my new site “0000abc123.com” …..

Will hyperlinks within the site’s page content auto update to the new domain name?

Example : “Click here to see this page” (0000abc123.com/page1)

once i point the domain over will it auto update to:

“Click here to see this page” (mydomain.com/page1)

Or will I have to replace them manually?

I have heard of the search and replace plug-in. Is this the scenario that tool is usd for?

Thanks!