WellNo, no you can't do that.
Short answerAlternatives: Either Either you find some other free mail service like outlook.com for your domain, or you create a mailbox elsewhere and forward to your gmailGmail inbox. Sending from your Gmail account under a different address is possible because you can set SMTP to a different provider in the Gmail settings.
Long answerReason: If you want to use your own domain with standardfree gmail, you have to create the email address and mailbox elsewhere and then forward those emails to your Google inbox or access them through POP3.
Simply pointing your MX to Google does nothing because GoogleGmail is not set up to receive mails directed at your domain. It takes both: Setting the MX records and letting googleGoogle know that it is the recipient of your MX records. This is what you do in the Google Apps Control Panel when you sign ofon with your domain.
Since googleGoogle won't let you do that with a standard gmailGmail account, it's not possible.