Certainly!
Lets take the (Obviously extreme, but bear with me, I am going somewhere with this) hypothetical situation where the Magic the Gathering team makes the creative decision to have the next block take place in the plane of "Playboy Mansion", all of the creatures and planeswalkers would be unclothed and the equipment would be toys. Meanwhile, the D&D team decides to release a "Complete guide to urban warfare and interrogation techniques" complete with descriptions of using Delayed Blast Fireball IUD's and well researched sections on how to inflict pain.
Similiarly, lets say that Avalon Hill decides it is going to create a boardgame targeted at some ultra-niche market. Lets say a wargame representation of the storming of Normandy which requires the player to control every single combatant as a seperate game piece with a rulebook that is so in depth it is hundreds of pages long, with a potential market of fewer than 1000 people worldwide.
Would Hasbro allow any of those products to make it to market? I can't imagine they would. They'd exercise their ability to block those products and tell the teams to come up with a different creative direction. Hasbro only stays out of the creative process so long as the teams follow a set of rules, and Hasbro guides the creative process by possessing the ability to veto any given product or constrain the budget to reduce or eliminate the ability to produce some product. As such, any creative decision is made based on the understanding that Hasbro has certain expectations on the content of the product, and the potential penetration of a product.
Hasbro only stays out of the creative process only so long as corporate expectations are followed, if the creative process would yield a product that would be controversial and harmful to the parent company's image, harm the future of the brand, or have a negative profit to expense ratio, I cannot imagine that Hasbro would not immediately become involved. Someone is reporting to them, someone is getting their marching orders from them.
So what I'm trying to say is that there's many ways to be involved in the creative process, and I can't imagine that Hasbro doesn't exercise high level input.