Is the title Tropic Thunder a play on words?

According to "9 Odd Facts About ‘Tropic Thunder’ That Will Change the Way You Watch the Movie" by the GuySpeed editors:

The movie title is a play on "Tropic Lightning", which is the nickname of the 25th Infantry Division which has seen action in WWII, Korea, Vietnam, Southwest Asia and Iraq. The same division is also featured in the movies The Thin Red Line and Platoon and includes former members such as Oliver Stone and Ice-T

The same is said here.

More information about this division:

The U.S. Army's 25th Infantry Division, nicknamed "Tropic Lightning," is headquartered at Schofield Barracks, Hawaii and is assigned to the Pacific Command. The Division of nearly 17,000 soldiers stationed in Hawaii, at Fort Wainwright and Fort Richardson, Alaska, focuses primarily on training for low intensity conflicts throughout the Pacific region.

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The division's shoulder patch, a lightning bolt superimposed on a taro leaf, was formally adopted in 1943. The colors of gold and red were those of the late Hawaiian monarchy. While soldiers over the years have jokingly nicknamed the patch the "Electric Chili Pepper" or the "Electric Strawberry," in 1953, the nickname "Tropic Lightning" was officially adopted.