Technically, the RAT powers the blue hydraullic system which will power the hydraullic driven emergency generator. There is enough hyd and elec power to keep the airaft flying.
However, the winmilling engines will continue to generate enough hyd power for quite a while. In the simulator we use, there's enough airflow through the engines to keep enough hyd power down to about 180 knots. But a mate who had a winmilling engine situation for real said the hyd low pressure ECAM for that engine didn't come on until they had slowed to about 80 knots on the runway.
As for Boeings, I only have experience of the 747 (Both classic and 400). There was no emergency hyd generation at all in the case of a 4 eng flameout - and no RAT. There were air driven pumps for 2 engines (400) all engines (Classic) but you couldn't start the APU in flight, so you were screwed. However, there were a few cases of 4 engine flameouts being survived in the 747 and I can only assume that there was enough windmilling hyd pressure to keep the aircraft flying. Interstingly, the 747-8 does have a RAT.