Not necessarily, because they'll leak revenue from the foreign broadcasting contracts and the sponsorship contracts, should they fail to meet the on-pitch performance benchmarks (like CL) in the contracts. There's also the problem of how much, and how quickly, they take a financial hit from kit sales/matchday. The timing is suspicious in the sense that I would bet a large chunk of their kit sale revenue happens in July and early August. They're also selling a lot of kit overseas in places where this story might appear on the front page for a day, then vanish.
Long run, you're probably right that the PR hit will do more damage to future sponsorship contracts than they save now, but they're not in a position to think long-term. They're losing $100M a year, and have a decaying stadium they'll have to do something about sooner rather than later.