I was addressing only the forwarding part of your plan. If you care about your free Gmail emails being scanned and you forward it… it’s still being scanned
I personally wouldn’t rely primarily on Apple’s email system as a replacement. I’ve been wary of using iCloud Mail as a primary because of overly-aggressive spam filtering - and especially blocking mail without telling users. This 2012 story describes secret blocking that refused to deliver a file containing the sentence “All my children are barely legal teens – why would I want to let them drive by themselves?”
Later in 2013 MacWorld confirmed that text or even ZIPed PDF files that contained the nearby words ‘barely legal teens’ would simply be blocked from delivery to iCloud Mail accounts.
Apple never publicly addressed this issue, and I don’t know if it continues to block specific phrases like that. Regardless, Apple does continue to cull what it thinks is spam so that it does not even reach the iCloud Spam folder, so there is always a possibility that you will not get mail sent to you.