Some time customer/clients are not a technical expert, especially one in a managerial or administrative position. They will make some wrong decision and as tech support executive, you will get pissed off.
Someone ordered SSL cert for www.domain.com and now if you want to work it for order.domain.com. It will not work as SSL certificate are domain specific. For example, SSL certificate issued for domain nixcraft.in is valid for nixcraft.in domain and not for demo.nixcraft.in or order.nixcraft.in sub domain.
In short, answer is no. However, you can obtain wildcard SSL certificate that is good for sub domains. It can be used with *.nixcraft.in domain.
Therefore, you can use it with order.nixcraft.in as well as demo.nixcraft.in without any problem (if you order wild card cert).
I guess it is a good idea to consult tech support before making any decision which can cost you money as well as time ;)