Any offline client will do; I use Claws Mail since ages where I migrated all my email also from past clients such as Eudora under Windows XP. http://www.claws-mail.org/
It's multiplatform, very fast and stable and can keep, index and search huge datasets of emails (mine is over 60K messages since mid 90s) in seconds. Backing up/exporting the email database needs only saving the Mail directory in the user's home; I've successfully moved mail directories between Linux and Windows installations of Claws Mail without a hitch. It made Outlook users drop their jaws when they realized how fast it is and they no longer needed to delete years of mails because the client became slow as molasses.
All you have to do is configure it to access Google servers like any other client then check the option to delete the mail on the server once it has been downloaded. IIRC this option is checked by default.
I used it for a grepping through years of emails.