Short answer: *Yes, i stronlgy believe that should not be a problem.
You dont mentioned _What_ wireless card you actually have, so this is just the basics.
1) You have to check your /etc/wpa_supplicant.conf file, if what's in it is correct. (e.g essid, password, encryption type as for instance preshared key)
2) You will have to know what command in console starts your wlan up.
iwconfig wlan0 up
then you need to start the wpa_supplicant with correct paramters.
The couple of lines which you find fire up your device (e.g check with ifconfig & iwconfig) and ofc try to ping some page.
needs to be inserted into an init script (so that it starts upon boot process) i guess linuxMCE shouldnt have any issues then if the network card is initialized before it launches. if so everything can be fixed :-)