I mean, "push" has become more of a marketing term than a technical one. If we're talking marketing, sure, call it whatever you like.
But the technical distinction between the two holds. If you subscribe to an RSS feed and then never launch your reader again, nothing happens. If you subscribe to a newsletter and never check your inbox, your inbox still fills up.
I really don't see the difference you're trying to make. The RSS reader would also "fill up" in the sense that if you open it all the items would be marked unread just like in the inbox. Personally I use my inbox as my RSS reader by using a service that forwards RSS feeds to my inbox.
Everything is just a feed, email, RSS clients, social media, messaging apps, notifications channels. It's just a matter of managing which ones you make a habit of visiting and being notified about.
The local RSS reader you never launch is not executing. It does nothing - does not pull content. Nothing happens - no bits are transferred over the wire, nothing is written to disk until you initiate the pulls by launching the app.
Email servers operate continuously, so that when some publisher sends ("pushes") an email, that is delivered to your inbox, which will eventually fill up your quota (or the disk).
You can blur the distinction of what happens from the user's perspective all you like, and that's why I mentioned marketing phrasing. But it does not change what is actually happening.
Actually, under the IMAP protocol a client will make a connection and keep it open while the server pushes notifications about emails that have been pushed to the server, at which point the client will make the decision whether to transfer the mails to the client (or delete etc).
There's also the newer variant, PUSH IMAP. I think that one speaks for itself.
But the technical distinction between the two holds. If you subscribe to an RSS feed and then never launch your reader again, nothing happens. If you subscribe to a newsletter and never check your inbox, your inbox still fills up.