Yes - it's entirely possible to have your Mac send and receive iMessage using your iPhone's message as the "caller ID" only.
Setting this up is normally a two step process.
First ensure that your phone with the number you wish all computers to use as your "caller ID" for the Mac has your Apple ID enabled for Messages. Until that device has activated the phone number to your Apple ID account, you can't go to step two.
Next, in the preferences on your Mac, look at the bottom of the pane for that Apple ID and choose to send a message from your Phone number rather than from the Apple ID mail address.
I prepared that picture for another answer and you might read there in case things are not working. I find it best to set each and every device to send from the same one string - whether it's a string of phone digits or a string of email address to avoid having people reply to your non-preferred account. In that case, you can either deal with two conversations or train them to send to your preferred address. It's a bit of tough love, but the most effective way is to only accept messages from your preferred string and then send read receipts. That way people realize some messages do not get delivered and self correct.
Apple has a nice article that covers how things are supposed to work as well as what to do when things don't.