The type of connection that you use to access the internet has nothing to do with mIRC.
You run mIRC on your computer (noting as how you're referencing an aircard, I'm going to presume that the computer is a laptop), and use your computer's internet connection to access an irc network.
Since you were able to connect to the network (as must be the case in order for you to get onto a channel, as well as DCC get), then you've answered your own question.
The fact that you were unable to DCC send can have many reasons, one of the most common being that the your local host information was not set correctly when you connected to the network. Try reconnecting to the network.