It seems counterintuitive to me to use a site removal feature in the Google Search Console when migrating a site from domain A to domain B. But one SEO asked if it would help in a Google Webmaster Help thread. The answer is obviously no.
If you have 301 redirects in place from domain A to domain B, using the site removal tool will enforce that Google doesn't pick up on those redirects. In fact, it would seem to me that it might slow the site migration process, rather than speed it up.
Google's John Mueller said in the thread:
The site removal feature in Search Console won't speed up a site-move, it'll just remove the old site even if we haven't fully indexed the new one. Since the old URLs are redirecting, it's best to just let the old URLs remain indexed (until they move over in the index), as users can still click through and reach the new site that way.
So, generally, stay away from using that tool for site migrations. Of course, maybe if your site is slammed with penalties you may want to try it but otherwise, stay away.
Forum discussion at Google Webmaster Help.