I have a Dahon, with 20" wheels, that I have used on a few evening club rides.
This was the bike I was using when I started to ride more, and, before joining ICC, I'd ridden it around Richmond Park on quite a few occasions (and a little further). Later, for novelty, I tried out a solo ride on ICC's NLH route, and a few evening rides when my other bike was damaged.
I did notice the difference.
The bike is, I think, marginally heavier than the 13kg tourer that I normally use, and which, itself, can probably be considered a heavy choice. I think that a 6-speed Brompton will be similarly heavier than most (basic) road bikes used by ICC members.
The larger issue was position and, I think, some more resistance to motion. I found climbing a lot harder. More effort was required in order keep up with others.
For regular club rides, I'd not consider my folder a good choice. While some ICC rides can be quite gentle, our less brisk groups can still move along at a pretty good pace (12-14mph average moving speed).
I'd suggest that, unless one is quite strong, or, at least, very familiar with club ride pace & distance, it's a good idea to make rides easier rather than harder. For initial rides, it is probably wise to be careful with choices of bike, shoes/clothing, and food & drink.
A good alternative is to come along to a Regent's Park group skills session, or possibly to meet people at the Cafe after Saturday morning laps, and get a feel for some of the riding (though laps are not so representative of Sunday rides).