If you Bought him for the MP then Yes You can claim them on ANY Toon. IF you Bought them with Marks of Legend then Sadly you do NOT get a free unlock, You must earn the Makrs and buy again on a diff Toon.
Ahh Ok Classic Batman Was Never on the Marketplace. He was a Buy with MoL ONLY. Urgo you must earn the marks on Every Toon to own him