Can Gargantua/Pantagruel trigger the Horizon Signal event once the infinity machine is gone?

[Marth Vader]

Pretty much the title. I made an empire with the idea of rushing the worm-in-waiting, and of course the only black hole anywhere near me turns out to be Gargantua. Can I trigger the event after the infinity machine is gone?

[adobo]

Pretty sure the Infinity Machine system itself isn't a trigger.