The confusion here may be the following...
It is not possible to set up a POP account on your iPad mail.app and gain access to the complete history of your Drafts and Sent emails which may ALREADY be on your service providers servers.
It IS possible to use a POP account in the iPad mail.app and have Drafts and Send emails saved into those folders once you start using the iPad for email. Even then, those folders do not necessarily get synchronised with your service provider so that you can see those draft and sent emails on other clients.
This is a general limitation of using POP and is true for any basic mail setup on any device and is absolutely nothing to do with Apple or the iPad specifically.
If you need "full feature" email then I suggest you switch the account to IMAP. Most service providers allow that these days on everything but the most basic of email services, so you should definitely look into it. Once you have IMAP (or similar) enabled you will be able to enjoy the full features of folders etc. from your iPad mail.app and you should see everything seamlessly integrated with other computers.
