Martin Berkhan suggests to supplement with BCAAs pre-workout when training in a fasted state. If a person plans to continue a fast after a workout (typical for us morning trainers) he suggests supplementing with BCAAs every couple hours post-workout. I do this on occasion when I workout around 6:00 AM, and then continue my fast until about 12:00 PM or so. During this time I will supplement with 10 grams of BCAA every couple hours until the fast is over. The reason for this BCAA protocol is to stimulate protein synthesis and metabolism.
Although, you could do the BCAA supplementation throughout the entire day (until 6:00 PM with your current described schedule), I wouldn't necessarily recommend it. In my opinion, your best bet would be to workout after work at the end of your fast (possibly experiment with BCAA pre-workout), and eat your meal afterwards. I feel that strategy would give you the best results.