Email everywhere?

[Platypus]

What do you mean by "configure [Gmail] to use localcompany's SMTP server"? What is "Gmail" in that scenario - an app, the web interface?

If I send mail from my Android phone it sends as me@mydomain.com, not me.mydomain@gmail.com, so it all works. Same if I use Thunderbird on my PC, and same if I use the web interface.

Gmail as in the web interface through a browser at this point.
Gmail has the ability to "Send Mail As" someone other than the default me@gmail.com address. When you add a "Send Mail As" account, you have an option to "Send through Gmail (easier to set up)" or to "Send through me@mydomain.com SMTP servers".

I'm talking about doping the latter, not the former.

I have no idea why you think, or why you think I think, that your email might be sent as you.yourdomain@gmail.com

[Bunk]

What do you mean by "configure [Gmail] to use localcompany's SMTP server"? What is "Gmail" in that scenario - an app, the web interface?

If I send mail from my Android phone it sends as me@mydomain.com, not me.mydomain@gmail.com, so it all works. Same if I use Thunderbird on my PC, and same if I use the web interface.

As far as I understand it, Gmail is working as a client for the other email account.

[Platypus]

Won't one of the problems with IMAP be that if one user deletes an email then it will get deleted on the server and from everyone else's devices?

Or is this not an issue with IMAP?

I think that's absolutely an issue with IMAP