Can I informally ask the special session organizers about the paper's decision? I have sent a paper to a special session of a conference, and the notifications will be given in one week. 

But I have to send my publication list for a postdoc position this week. Do you think it'd be a good idea to send an informal email to the organizers asking if the decisions have already been taken?
Yes, you can certainly ask, but you may not get an answer, especially in the time frame you need. So, when you ask, say why you need the information. 

But even if you don't get an answer, you can list the paper in your CV as "submitted, awaiting decision", so that you get some "credit" for it. But, since decisions about the postdoc won't be made for a while, anyway, you can probably update your cv when you learn more.