That I don't know. I've never tried it without having a printer available immediately. I would think the boarding passes would expire when the Internet browser session was ended, or exited. I could be wrong, though.
If this is true, though, I know a way around it:
Save the boarding pass page as an Adobe Acrobat Reader file, or pdf, get that pdf to some other computer with a printer attached and print it out there. I've never needed to print out a boarding pass via pdf like this, but I have saved boarding passes to pdf before and kept them on my computer, as a precautionary measure which has so far never proven necessary.
It seems like at the airport, you would get whatever boarding pass is available at the time you arrive and print it out.