Can I assume this means we do not get the +2 bonus when wielding two-handed weapons such as a pike, glaive or halberd?
Correct, because the character is now holding a melee weapon with two hands (ergo, in two hands). The character doesn't get a pass on this just because there is only one weapon entity. This is different from wielding a sword in one hand and a shield in another because only one of those counts as a weapon.
This also means that when they use the versatile feature of a battleaxe (changing a d8 to a d10), they lose the benefits of the dueling style because they're now gripping the weapon with two hands.