Posted 06 May 2013 - 01:48
you need to understand how dns works:
if something wants to communicate with you, it needs to figure out what the actual "address" is using your domain which is basically just a short hand. so you designate a name server that acts as a directory which lists all the actual addresses. it also allows you to list other records, like TXT for example.
so to get to your website, i'd have to reach your DNS, and ask it where your website is located, this is the A or AAAA record, the DNS tells me that IP and I can proceed to go there and get the actual page. to send you mail, I have to ask your DNS where your mail server is, this is your MX record. Once I get that, I go on over to wheverer I'm told then ask them to receive my mail.
What you apparently did, is in your registrar's settings, you designated HostGator as your DNS server. That means people are asking HostGator where to go. And you made the appropriate records in HostGator to tell them to go to Google for emails.
So if you decide to switch email providers, just update your MX record at whoever is your name server, and point it to the new service. That means you can switch DNS and keep using Google for email by just keep pointing people to them. If you want to cancel HostGator, you obviously can't keep using it as your name server. You'd have to designate someone else as your DNS and make the appropriate records there. Likely, you'd simply use your registrar as the DNS, so you'd just have to make the right records there for it to work.