Having asked similar questions recently this is what I've found. The bar clamp height is slightly higher on the H stem than the S stem, both the M & P stems are lower than these. So the highest bar position is via the H stem and it has more reach than M&P but 13mm less reach than the S.
So if you put flat bars in an H stem then you would be raising them slightly over an S stem but also reducing the reach.
However the H stem hinges higher up and therefore when folded the flat bars would be further from the ground than with an S stem.
This means that if you wanted to use wider/riser bars then the H stem would give you more room, I particularly liked a stem riser solution suggest by the all knowing Kim on YACF:-
http://www.ebay.com/itm/LitePro-Bic...-Folding-Bike-Light-Weight-Stem-/271290827931
This allows you to use flat bars but get the benefit of a riser bar, so you still have plenty of grip/bar area for additions. You can also angle slightly to account for the 13mm reach loss.
Cables would probably need to be adjusted to suit.