DirSync with default domain .onmicrosoft.com

Hello All -

I have a default domain in Office 365 called <MyDomain>.onmicrosoft.com. I would like to try out the DirSync option with my on-premise AD and Exchange 2010 SP3.

On-premise AD domain is Mydomain.com. This is not a registered domain is only used for development purpose.

Now is it possible to achieve DirSync with the above?  Is it mandatory to register a domain, validate it in Office 365 portal to achieve DirSync.