Yeah him and McDonnell would be going through the division lobby with him for sure on EU matters. Apart from votes on Europe that could force the toppling of the Tory government (he’s voted consistently, I think, with the whip on those particular votes).
But yes many of the old school “Bennite” left (not sure Skinner’s a Bennite tbf, he’s a law unto himself really) are intrinsically Eurosceptic and I’m surprised that anyone would still be surprised about this. Luckily for Labour at the moment whilst Corbyn’s ideological persuasion is anti-EU, it’s not an issue which is of particular importance to him.