No. You cannot. Perhaps you'll know the others with their new posts and stories while you put your CHATBOX offline.
If you mean the Facebook chat, no there is no way for you to appear offline / invisible like you would on Skype, MSN, etc.. If you mean the social stream on FB, showing what people are liking/etc. then the answer is yes.
Well if you had a smart phone you dont have to be online but you still get all the updates and that good stuff!