let's get some things straight, guys;
POP3 downloads messages from a server. if you've enabled your client to leave the messages on the server, all clients connecting to the server will have access to the email. in a POP3 situation, you can delete, move and edit your mail through your client and it will NOT affect the messages on the server. all other clients conneting to the server will get the original message, provided you chose to leave the message on the server after downloading.
IMAP does NOT exhibit this behavior. IMAP allows a "two-way" communication between client and server. if the client deletes and email or moves it to trash, the same will occur on the server.
both of these apply to the default email client, the gmail client, k9 or anything else. period.