It’s very rare for someone to do a club ride on anything other than a drop bar road bike. You do see the occasional flat bar road bike/hybrid but that’s as exotic as it gets. I have a very well-travelled 6 speed Brompton and have never done a club ride on it (though I have done the 200 km Great Escape on it).
I think you might be ok on the Intro ride, but only if you can keep up with the group and only if you intended to switch to a road bike in due course.
I say that because club rides work best when everyone rides in a tight group at a well matched pace and I think having a bike of such a different shape and with different speed characteristics makes that much harder.
(If you want to do longer/social rides on your Brompton, can I point you towards London Brompton Club on Facebook)