Yes they will, but they won't be being protected by avast.
Why can't they be changed? Is there an error message
![Huh ???](https://forum.avast.com/Smileys/default/huh.gif)
avast doesn't stop you changing email account settings!
By your other accounts are you talking about sending, if so have you ticked my server needs authentication, etc. ? are they webbased email accounts, such as hotmail?