Of course, if I am away from home and work mail, I have no way of syncing what I received and sent with my main computer. This wold be vitally important if legal affairs were at stake.
Email account mailboxes and messages are not included with the iTunes sync process, which isn't required with an IMAP account such as your MobileMe account. All server stored mailboxes with an IMAP account are kept synchronized with the server automatically with each email client used to access the account as long as you have internet access.
With a POP account, all new messages received at the incoming mail server are downloaded by the email client used to access the account. No mailboxes and messages with a POP account are kept synchronized. Although it is possible to access a POP account with more than one email client, a POP account is designed to be accessed with a single email client only. An IMAP account is specifically designed to be accessed with more than one email client.
Since you are away from home, which internet service provider are you using with your iPad via the available wi-fi network your iPad is connected to? If your POP account does not have an authenticated SMTP server and if the account is provided by your internet service provider used at home and you are connected to another internet service provider at the present time is why you can't send messages with your POP account. The reason you can send with your MobileMe account is because your MobileMe account has an authenticated SMTP server.
You can't use the MobileMe authenticated SMTP server to send messages with any other account. It can be used to send messages with your MobileMe account only.