My Neighbours do and they make a sauce to go on their icecream and so on, so I think you would be ok, but wait and see what someone else says first.
Oh! I also have one growing in my prevett hedge too, must of come from my neighbours when the flowers went to seed or from a little bird lol

No problem - it's a different plant, with a different root system. It can't be contaminated in any way from the privet.

You can make a lovely elderflower cordial using flowers, delicious.

maybe wrong but privet berries are similar in colour to elderberries, altjough not in size. Just a point, maybe stating obvious thou!