The bars will go forward slightly - and by slightly I mean about 1cm.
I tried this when I had one on hire, more to make the bike longer rather than drop the bars. And the bars then don't clip in when folded.
At the risk of continually repeating myself, I had exactly the same problem and ended up buying an H type (same stem height as S type, but with M bars) and removing the bars and fitting some riser bars. You can also do this to an S type.
The reason I went for an H type as a starting point is that the fold is ever so slightly higher and I was worried that the bar ends might catch the floor otherwise. Plus there can be a concern that if you do fit risers then the cables will be too short. And I figured it would be easier to shorten existing cables than to have to buy new, longer ones.
It's certainly an option worth looking in to.