I've completely moved all of my email accounts away from google and to my own server because I got tired of their nags telling me that none of my devices were using their email app. You can't opt out, you can't unsub, you can't get google to stop.
I'm also going to lose my yahoo email account soon which I only have because they bought geocities way back in the day. I don't use it for hardly anything but I refuse to accept their new terms because they want to have permission to read everything for analytics.
I have a couple sites I have hosted and email servers come with them. So if you want to call that "your own", it's pretty easy. Not free, by any means but you have full control and can make email addresses all day long. Want to enter into a contest but you're pretty sure it's a spam list? Make an address just for that, delete it when you're done. And so on.
As for your own physical email server, you need a box, a domain of your choic... you know, here's a tutorial on how to do it with a raspberry pi (dirt cheap and almost no power usage): https://samhobbs.co.uk/raspberry-pi-email-server
So a raspberry pi is a one time $35 (or cheaper) and the domain name is like $12 a year. If you want SSL, you gotta pay for that.
But to answer your question directly: extremely practical. There's no reason why you can't if you have any inkling of doing so.
By accessing your Google account from an unknown device, they know things such as your IP and device details. By sending a push notice to your phone they can have the Google app automatically respond, one example is the Google verification app asking if it's really you logging in, another is Gmail notifying you of new mails. In any case, when nothing responds they know your mobile device doesn't have g apps installed.
It's all done server side, your device isn't leaking more than any other device.
What you could do is set up your own email server (there's easy solutions available, any noob should be able to do it, there's visual "click here, select server name. Want SSL? OK, all done" solutions for less than 2 dollars a month, have Gmail automatically forward all new mails to your personal server and reply to all incoming messages that you've changed email address.
A few months ago I purchased a Samsung Galaxy A7 with the full intention of De-Googling my phone. I installed LineageOS without the Google Apps and I purchased a completely new SIM card that was not associated with my previous google activities. Aside from YouTube, which I accessed with NewPipe, I didn't use a single Google application or service.
Last week, I found out that my bosses boss was still using my old GMail and had sent some fairly important messages to my old account. Rather than waiting several days for my technologically inept boss to resend the emails, I figured "Fuck it, what's the worst that can happen?" and I checked my old GMail using K-9 Mail. I instantly received an Email from Google warning me about an unknown device logging into my account, which I confirmed as safe. Then I immediately received another Email announcing that my phone was not running Google Apps and it offered me a huge ass list of programs that I could be running.
I know that Google owns and develops the Android Open Source Project, but it's still surprising that they could find out my device was Google free after I checked a few emails.