The answer is Yes and No
Yes, the card will work, but you will not receive any of the premium channels, Movies, Sports etc...
Your Viewing card is paired with your receiver, the only way to continue to receive all channels at another location is to take your receiver with you
It should matter if it's not plugged into the phone line for a few days.
You don't need the phone plugged in in order to receive all your channels, however, sky do periodically tell the sat box to call out and pick up software updates etc.
Yes, you could ring sky and ask them to repair the card with the new receiver and get all the channels, however, when you get home, you'd have the same problem again, you'd then have to phone sky back and ask them to repair with your home receiver, I think they might get a bit miffed about that eventually LOL
You could try getting a multiroom subscription, however they normally like both boxes plugged into the phone line.
I did do this for a while, until they cottoned on and wanted to know why the second box was not connected to the phone
Else, if you can do without the premium channels, then you could just take the card and install in another receiver.
Hope this helps