I can't speak in unequivocal terms here but if your e-mail account(s) is an IMAP account there should be no problem removing it and adding back because an IMAP account is in sync with the ESP hosting it.
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Spinning beach balls in Mail, I would do a command-alt-zero to bring up the activity window.
You may want to eventually force quit mail, I do sometimes too don't worry. After doing that though, launch mail and perhaps rebuild your mailboxes.
-Restart your mac.
-launch ONLY mail - Quit other apps while testing
-does the spinning beachball persist? give it a few minutes to see
-If it persists and you have the activity window it mail reveal something stuck in queue and that could be useful to know about.
Sorry if repeated some things that BDAqua mentioned (he's too good), I was just typing away and too lazy to edit now or too tired rather (late at night here)
report back please.