Yes, I did that and had no issues and no outages. I use Google Domains (google.com/domains) though other hosts like Hover have been good as well. Google explains the setup pretty clearly. I always time this either for a weekend or end of day just in case.
If you need any info on the domain setup let me know - as I recall it was very straightforward and I just copied their instructions from Google Apps (which they may now call Google For Work or somesuch).
I also configured my domain so mail.s-consult.com would automatically point me to my email inbox.