Actually, I think you do have to set up an @me.com account. See my comment here:
Sorry, I answered too soon. With more hunt-and-peck troubleshooting, I got it to work!
On your iPhone, go to Settings.
Select "Mail, Cotacts, Calendars."
Select your gmail account.
Set Notes to the On position.
Now on your Mac, go to the Mail app. Make sure the mail box side-bar is visible by clicking Show in the upper left hand corner, then go down to Notes and click the little arrow for drop-down items. You'll see a choices for On My Mac and also for Gmail. Your new gmail notes should show up in this folder. I have my notes folder on my mail toolbar and can do the drop down there. Hope this helps.