That is a good question! That depends on what type of air cleaner it is.
There is an oval air cleaner and then there is a round one that seals to the hood. The oval air cleaner should work but I can’t confirm whether the hood sealing air cleaner will work or not. I would need a stock intake to compare the dimensions with our cross ram intake. The fitment is so exact with that setup that any variation in design would likely cause it not to work.
My gut feeling is that the Offenhauser cross ram is a low profile manifold which typically means it sits lower than the stock manifold. Because of this I would say that it probably won’t work with the hood sealing air cleaner as the manifold surface is different than the stock manifold. That being said, it may still work with a spacer or carb riser if the positioning lines up correctly.
Hope this helps you.