Yes you can, I assume you are using the Titan Sentinel, while in City of Heroes you call up your character information from the options menu while playing. I always click on the badge tab after I have it up, but I have been told I don't have to do that. This is all done within City of Heroes itself, by bringing up the character info you give the Sentinel client what it needs to know.
Once you have done that Titan Sentinel should update automatically next time you check in, but you can ask it do under the options menu in the Titan Sentinel client.
Cool, good to know, thanks! That will make figuring out what I have/need for accolades a lot easier. 
Make a man a fire and keep him warm for the day, SET a man on fire and keep him warm for the rest of his life.
Incarnates: K'lir(Fire/Dark Corr):Hot-House Flower(Plant/Fire Dom):Kinrad X(Kin/Rad Def):Itsy-Bitsy Spider(Crab):Two Ton Tony(Mace/WP Broot):Teeny Weeny Widow(Fortunata/Widow) : Zeroth Law (Ice/Fire Tank)
Yep. Also in the City Info Tracker site they have a low hanging fruit report that I find to be a great help on my badge hunting characters. It list the most common badges available that your character does not have yet.
I just started using this program, and am curious how the badge functionality works? It looks like if a character gets a badge while I am connected, it shows up on the website, but if it is an older character with existing badges they do not show up.
Is there a way to force all the badges from a logged on character to the website, or do I have to check them off manually?
Make a man a fire and keep him warm for the day, SET a man on fire and keep him warm for the rest of his life.
Incarnates: K'lir(Fire/Dark Corr):Hot-House Flower(Plant/Fire Dom):Kinrad X(Kin/Rad Def):Itsy-Bitsy Spider(Crab):Two Ton Tony(Mace/WP Broot):Teeny Weeny Widow(Fortunata/Widow) : Zeroth Law (Ice/Fire Tank)