If they have a active wireless network and router in the house, and your laptop is equipped to receive 802.11 (a,b, and/or g) signals without a card, then no, you won't need a card. It there is an active network, but you don't have built in Wi-Fi in your computer, then you will need a card.

If there is not wireless network in the house, then you can always get online with one of wireless services offered by cellular providers like Verizon, Sprint, etc. Then you would need one of there cards, which is completely different than the wireless network card I just described. But this also assumes that the cellular provider's signal can reach your relatives condo.