The Yakuza is far too prominent in real-world Japan as if they would get a foot through the door of Gensokyo. And if they would try anyway, I trust Yukari would have one surprise or another waiting for them.
On the other hand, the Yakuza as a modern embodiment of Japan's feudal system might haven some embodiment in Gensokyo, even if this part would be more about being honor-bound rather than gathering as many whores around you in the local bar in order to display your social status.
PS: Yakuza is a laughable portrayal of the actual Yakuza. No integrity, no honor - just drugs, hookers, and moneys. Not much different from the Mexican drug cartels who are all devout Catholics but still will skin you alive for the slightest transgression.