Most headliners these days are just pressed cardboard with the material glued on. If you steam clean it I think you will probably cause the thing to warp and the glue will probably fail causing the material to seperate. Have you considered just replacing it?
i steamed the headliner in my 92 blazer which is kinda similar feeling to the one in my 00 gt but i have no knowledge if they are even remotely the same materials. it worked well but you have to do it in sections and make sure you completely dry it.. i used one of my wifes old hairdryers to speed up the drying process since i didn't want the adhesive that holds material to the shell to sag..
that was last year i steamed it, and no problems since. just take your time and go slow and you should be ok.