It's possible. This is typical behavior for a POP3 account.
If your account is a POP account, it's difficult to keep things in sync. Check to see if your email provider has an IMAP server, then switch both the iPad and Outlook to that server. Make sure you set up your mailboxes on the server in Outlook (instead of local), and your folders should stay in sync.
Also, or IMAP accounts on the iPad it is possible to delve into the advanced settings and make sure standard folders (Sent, Draft, Trash) are stored on the server, not locally. Any folder you create will automatically be on the server.