Today is my first day at work with the Pre. I generally work on websites while having a tab sit open with Gmail pulled up so I can see when I have new emails as well as any chat messages. This morning my first chat message came in and my phone chimed. I looked, and sure enough both my browser tab and my Pre picked up the new message. I began talking on the computer to the person via Gmail chat and the Pre stopped intercepting the messages. After about a half hour of inactivity between our convo, the person sent me another message and both the browser and my Pre received the new message again. Also, everyone I have talked to on Gmail chat is reporting that the status I set on my Pre is taking precedence over the status I set via browser. If both are online it seems to allow either one to work while accepting new messages on both devices.
In the past with AIM, and other IM programs I have used, the computer (browser) would always take precedence over any mobile device that was logged on to the chat service. I am sure this is just an undeveloped option and will be provided in the near future.
For now, my work around is to simply sign off of Gmail chat by opening the Messaging app >> clicking Buddies tab >> clicking the green icon to the left of my Gmail chat status >> selecting the gray dot Offline. This logs me off of gmail chat. I just have to remember to sign back on when I leave work, I guess.