Yes, you should be able to put them in the door panel. I placed mine in the back (hatch area) though under the panel that covers my amp. Took some extra wire but I didn't want to risk having them come lose and vibrating in my door panel. I've seen a couple people mount theirs in the door panels though so should be fine.
Since these speakers are an exact fit of the recess for the factory speakers I had to drill 4 small holes for the mounting screws. Door panel is metal there so took a little bit of time but came out factory looking.
98 Red GTS - Corsa exhaust, Belanger Hi Flow Cats, Smooth tubes, K&N filters, Custom Stereo, Forgestar F14 wheels, BC Racing Coilovers, HOWE radiator, Tuned by Dan Lesser from Viper Specialty Performance.