I understand that many of the islands were forested, but just wondering if they were ever deployed.
They were in fact used! The Japanese carried out airborne landings in 1942 in support of their invasion of the Dutch East Indies, and American paratroopers made some landings in New Guinea in 1943. The commando units known as the Chindits and Merril's Marauders made airborne landings in the China-Burma-India Theatre, with the former carrying out two major long range deep penetration raids in 1943-44, Operations Longcloth and Thursday. Finally, further airborne landings were made to support the Invasions of the Philippine islands in 1944, most notably in the capture of Corregidor Island. The United States Marine Corps even had it's own parachute-trained regiment, the Paramarines, but these only saw combat on foot as conventional forces, in particular in the Guadalcanal Campaign of 1942.
The 11th Airborne was deployed in the pacific. The 11th consisted of parachute regiments and glider/infantry regiments. My father signed up for parachute training, as it paid $50.00 more per month, and was assigned to the 187th infantry regiment. They parachuted out of the gliders into the Philippines. The Japanese first used the term Rakkasan (falling umbrella men) for the parachuting 187th, the nickname that followed them and that they embraced.