A Brompton fixie does make sense to me.
When the Brompton is unfolded, the chainring and sprocket should be the furthest apart from each other, so as the link shows above, the chain can be fully extended and virtually straight both on top (for accel) and bottom (for decel). The chain tensioner just gets pulled into a useless position when unfolded, and then becomes useful to take up the chain slack as the bike is folded and the chainring and sprocket get closer.
Suspension can mess with chain slack, but in the Brompton's case, it's movement is minimal, and the rear triangle hinge is very close in line with the chainring and sprocket - so just normal fixie chain slack should handle it.
I'd be careful on corners though... the Brompton seems low to the ground and you might strike a pedal if leaned in enough.