As for the real world, their point of gravity would be somewhere between them. That is if they where normal rocky worlds that didn't completely fuse. But if they were alien made words that use exotic matter to generate gravity, then maybe it could work.
Well it is a cool thing all in itself.
what if its like haumea^2 and the cores are made of some goo and this makes a hole in middle and a donut around it
it is possible but the planet would be bulged i believe, and it wouldnt be really like this