Yes, you may us both webmail and POP or IMAP with a mail client. For instance many users use Outlook at home and work but when at another computer they may webmail. 
 
You should be aware that once a message is downloaded to your mail client it will no longer be available via WebMail unless your mail client is configured to leave messages on the server. Furthermore, once a message is deleted using WebMail it will no longer be available for download to your mail client. Clients should also note that only messages in their inboxes will be downloaded to their mail client.