It depends on the environment you have at work.
If your coworkers are just casual acquaintances you happen to see on a daily basis, then I'd say no, for reasons others have stated (bragging, etc).
However, if your coworkers are more like friends, where you share personal stories, things about your lives, hang out outside of work, and so on, then I see no ...
Let's say you're working for Facebook or similar social media before they were popular. But you can't be bothered with promoting the very service you're working on? Either:
you really don't care about the service, which is bad enough;
or maybe the service is so bad that it's going to be a disaster, that's even worse.
I'd say the first case is more ...