WebView's are typically just WebKit / Blink / Trident / whatever embedded anyway. So if you're going to embed Blink then you've already lost any significant memory savings you'd hope to make by avoiding Electron in the first place. Thus you might as well write the whole thing in Blink / Electron from the outset as that will also give you massive developer productivity gains (which it will - such is the sad state of desktop application development these days).

As for the HTTP client point; you can use a simple HTTP API (libcurl or whatever) to perform the webmail authentication but honestly you're in for a whole world of pain because it's really more than just a HTTP call. Ideally you'd want another webview for that as well. Oh how all those individual webviews are going to add significantly to your memory usage. You might as well consolidate them all into one...let's call that new WebView "Electron" shall we ;)