Correct. The PC just needs to be on with the Redirector running. I do not believe BES will care if the Redirector is just sitting there running on your desktop. It just generates mail forwarding via your Outlook profile. A BES admin might have some more insight for you on this point though. I say "try it and see".
I don't use the WebClient myself but I just logged in and checked. It's located under the "Options" section...
"Reply-to address
By default whenever someone replies to a message sent from your account, the reply will be sent to this address.
If a reply-to address is not provided, replies will be sent to your Sent From Address."
Now I am unsure if this actually makes the ORIGINAL message appear to COME from that account, but it does appear that it will direct replies accordingly. I would think that "Reply To" would actually change that field in the message header before sending but I have not tested it myself to see how it actually behaves.
[EDIT] Disregard that. Go to "Profile" and then click on "Sent From Address" to set that. Sorry.
[EDIT]Ok, I couldn't help myself. I got curious so I started playing with the WebClient. Basically, you can set the "From" address to be whatever you want. In fact, I think it might even be a BETTER idea to do so since you might not want someone knowing what your actual Blackberry WebClient address is. If they know it, they can send mail to it and it automatically gets forwarded to your device! Ouch!
Anyway, I set it to "noreply@donotsendhere.com". I generated a message on the BB and told it that I wanted it to go through the WebClient. It went through fine. Now before I sent, I chose the option "Set Reply To" on the BB. I played with a lot of stuff when I first got it so I think I might have this option due to installing BBReply on my handheld. Anyway, you select what you want the "Set Reply To" to be. When the e-mail shows up for someone, it says that it is "From" the "noreply@donotsendhere.com" address (the friendly name is listed as whatever you set in the WebClient. It could be "Sabre's Blackberry Device" if you like.) So even though that is not a valid address, when they click on "Reply", it "replies to" the address you have selected when you generated the mail on your BB device.
I could see how this would go a long way to assist those who have to rely on the WebClient only and don't have the option for the Redirector. I would definitely be doing it this way if I did not have the option of the Redirector myself. If you don't have the "Set Reply To" option when generating mail via the WebClient on the BB device then install the BBReply software. Hope this helps!