When the A320 went into the Hudson River, the Captain deviated from the checklist cadence and quite appropriately fired up the APU, more or less immediately after the birds hit.
This action kept electricals (and hydraulics?) and retained(?) the FBW mode as NORMAL Law (????)
Nonsense,
all aircraft I flew have enough hydraulic output from a windmilling engine at clean speeds. Below speeds of typically 160-180 hydraulics are lost. You notice every time with an engine out that once reducing below those speeds, the hyd "low press" lights (Boeing) or secondary HYD/FCTL failures (Airbus) will kick in. Also battery power is sufficient for flight controls and primary instruments.
APU start is still important, especially to keep your position awareness as navigation displays (moving map) remain displayed
BTW Airbus goes to alternate law as a result of the "both engines out" condition, regardless of whether hydraulics and electrics are retained.
Not relevant here as flare mode is the same for alternate laws 1 or 2 or normal law.