I've had three full size folders and I don't believe my speed on those versus my Brompton was any quicker over the same routes.
A rabbit.de folder - which took less than two seconds to fold.
(not mine BTW)
Then a Dahon Matrix Lockjaw. This took a little longer to fold as it needed an allen (hex) key.
Then, because that snapped, a SH Matrix which was the same fold as the Rabbit...
All the ones I've owned (and most of those I've seen) just fold in half, so the folded package is till relatively big. Some, the handlebars also come off or twist to make it narrower.
On a smooth surface over a relatively short distance, I genuinely don't believe anyone would be much faster on a 26" wheeled bike with flat bars and a more sit-up-and-beg riding position.
However, I'm about 3-4mph quicker on my road bike on the same routes. But... over a long distance, I reckon I'd tire more quickly on the Brompton - or on an MTB for that matter compared to a sorted road bike.