Likely, though it depends on the variety. Some will eat anything they can get, others are picky.
Yeah, washing off just removes the adults - it doesn't do anything for the eggs. If you think you can get ladybugs (on your own or otherwise), just keep washing the aphids off until you get some - any insecticide you use will also kill the ladybugs. Note it doesn't take a lot, as ladybugs are rather voracious eaters. If you don't think you can get ladybugs, however, you can use insecticidal soap or neem oil. Insecticidal soap is the safest if you have pods on the plants, but requires daily spraying not only until the aphids are no longer visible, but continually for at least a couple more weeks to ensure you get the emerging larvae.