Will either Live Mail or Gmail keep PN Mailboxes and permit IMAP?

[#1]

I am thinking of receiving/sending all my emails through Live Mail ot Gmail. As the title says, "Will either Live Mail or Gmail keep PN Mailboxes and permit IMAP"?
Is there any other potential snag with this course of action?

[#2]

Gmail allows you to "Send mail as" your current PN Mailboxes and permits IMAP.
No experience of Live Mail.

[#3]

Windows Live Mail also provides the option to use IMAP. See this page for set up guides (different for the 2011 and earlier versions). Choose IMAP (rather than POP3) when configuring the incoming mail server.
The outgoing server will still be relay.plus.net using authentication if you are not connected to a Plusnet connection. Or you could use an alternative outgoing server (eg gmail with suitable authentication).
You can set up whatever email address you want to use as "sender", generally these are called "identities" and you can define more than one with one of these set as the default.