The change you are seeing is a result of the way Avast works.
When Avast is not involved you see the gradual movement of the progress bar as your message is sent to your mail server. I assume you also get a final "Message sent successfully" message or something similar.
When Avast is scanning the mail your email program is "fooled" into thinking it is talking to the server when in fact the mail is just being sent to Avast inside your system to be scanned. Bacause this happens inside your system you see the progress bar move very quickly to 100%.
At that point Avast has scanned the message and Avast then takes over the job of sending the message blocks on to your mail server. When Avast has finished sending it passes back the final "ok" from the mail server to you email client - which should still give you the "Message sent successfully" response.
Untortunately, OE expects to hear back from time to time from the mail server it is sending the mail to and, because of the way Avast works, it does not. So, it issues the timeout message. It does not mean that the mail is not being sent out, it just means the OE is complaining - you can just say you wish to continue waiting and the mail will be delivered. Try setting OE's timeout to the maximum.
As a matter of interest, how long does it take to send the same message when you turn off the outbound mail scanning of Avast?