Depends what you mean by "allowed". If the rules say "you definitely can't do this", but there is no penalty for going ahead and doing it anyway, is it allowed?
I assume other than phishing it's also the poor UX of switching to your email inbox and then back to the browser, which can be especially bad on mobile.
That being said, I like the idea and have asked myself that question before as well.
We are looking for someone to join us on site, but depending on the Visa process, we are willing to help matching candidates with the process. And we have non-European team members.