Welcome aBoard, Jake; nice to have you. I think you're right. I have looked up the word and found these ref.'s:
gad·a·rene [ gáddə rn ]

adjective

fast and without thinking: rushing headlong en masse ( literary )

[Early 19th century. Via Latin < Greek Gadarēnos "inhabitant of Gadara," town in the Bible where a herd of swine rushed into the sea (Matthew 8:28)]
(Encarta® World English Dictionary)

Gadarene
/gaddreen/

• adjective involving or engaged in a headlong or disastrous rush.

— ORIGIN Greek Gadarenos ‘inhabitant of Gadara’, with reference to the story in the Gospel of Matthew of the swine that rushed down a steep cliff into the sea and drowned.
(Compact Oxford English Dictionary)

2 entries found for gadarene.

gadareneGadara

Main Entry: gad·a·rene
Pronunciation: 'ga-d&-"rEn
Function: adjective
Usage: often capitalized
Etymology: from the demon-possessed Gadarene swine in Matthew 8:28 that rushed into the sea
: HEADLONG, PRECIPITATE <a gadarene rush to the cities>
(M-W Online)

Gad·a·ra ( P ) Pronunciation Key (gdr-)

An ancient city of Palestine southeast of the Sea of Galilee. It was one of the Greek cities of the Decapolis.

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Gada·rene (gd-rn, gd-rn) adj. & n.
(AHD)


It seems to boil down to being used as an adjective vs. as a noun. I personally find it simpler to think of the noun as meaning a person from Gadara. I am not familiar with the word, but I can't help thinking it would sound funny to say someone did or made a gadarene.