For sending - yes.
For receiving - no.
You can only use one email server to receive messages for a given domain name. When it's a domain configured in your Mailgun account, it could be either Mailgun or Google/other servers, but not both.
Both is bad; servers get confused. Don't do both.
However, you can use the same domain for sending at multiple servers. If you’d like to register your domain at multiple servers for sending, but don’t want to receive email at Mailgun, this is simple - just don’t configure your MX records to point to Mailgun!
If you've got incoming emails setup elsewhere for your root domain, we recommend using a subdomain in your Mailgun account and pointing its MX records to Mailgun so you can also receive emails via our platform. The different hostname for the subdomain keeps DNS for the two domains separate. This helps improve deliverability, and allows us to more easily deal with any issues that arise with recipient email servers.
Without these MX records in place, you might see an increase in "Sender Domain Verification" errors, which are errors that the recipient server returns whenever your domain lacks MX records. By configuring your domain with MX records (either Mailgun's or an alternate incoming server) the "Sender Domain Verification" error gets a solution, and is prevented from occurring in future cases.
Sinch Mailgun has answers! If you have any concerns or questions, please send us a Support ticket using the Support page within your Mailgun Control Panel. Our Support Team will be happy to assist!