Back to your OP, "removing" an account from Mail will not change anything at all that she currently sees in iPhone Mail app. That said, if you are not absolutely certain that every message she needs to refer back to is in the iPhone, you might want to take pause and look into the Mac Mail settings further. In Mail > Preferences > Accounts, do all of her accounts show as "IMAP"?
If so, "delete" accounts all you want (in recent Mac OS X versions, Mail will redirect you to Syspref>Internet accounts where you can uncheck Mail for the given account; and actual deletion of messages is not immediate; nor is there a documented process to force your drive to delete downloaded messages for accounts that you deactivate). Anything that was in your On My Mac folders will remain untouched by removing/deactivating an IMAP account.
If any accounts are dotmac, rather than IMAP, you are in for more parsing of what she needs to keep (and then exporting mailboxes to save whatever is valuable on the Mac Mail for the dotmac accounts).
Now to your followup:
Yes, everything that has already been downloaded that belongs to those 17k messages will be in her TM restore. But they shouldn't impact restore time enough to warrant investing time in creating a "fresh" restore that has her Mac Mail accounts removed, however. The best rule of thumb is to just let TM do it's thing, or don't use TM at all.