Can a crack in a manifold cause an oil leak?

The answer is yes. A crack in a manifold is much worse than just the oil leak. Manifold cracks are generally caused by severe overheating or improper assembly of parts. A crack in a manifold can cause oil to leak but the oil leak is inconsequential as the crack renders the engine unusable safely, without replacing the manifold. Running an engine with a cracked manifold is very bad for the rest of the engine and your own safety.