Hi Rtrhead,
short version: no way
long version:
In normal circumstances, the FBW will switch into a so-called flare mode as you approach the ground (or water...) and will introduce a nose-down elevator input, forcing the pilot to actively input up-elevator to maintain attitude. So without pilot input, the aircraft would actually lower the nose and make contact at a higher rate of descent.
But this is only for normal OPS. If the FBW system switches into an alternative mode due to power loss, the handling changes (to a point where the sidestick deflection is proportional to evelator deflection) - but at no point will the FBW system automatically pitch up to a specific attitude in either modes.
I'm not sure in which mode the hudson bus was in, shortly before contact. Even if both generators tripped offline (due to low engine RPM), there is still the RAT (a small turbine which drops into the airstream to deliver electrical/hydraulic power to key systems) plus I think the FO started the APU as part of the drill - but not sure if it was online at that point. If so, the FBW system would have been in normal law the entire way down.