No they won't have FFP problems (yet), but they will have a massive selloff problem.
Imagine some of those players fail and don't play up to standard, so you try to sell them. However, you must post them at a very large price, say 60m GBP for example, because you still have to pay the rest of the transfer fees, but since you can't because that will cause you to jump over FFP, you have to pass them on to the next guy.
And since most clubs will not spend a ridiculous amount of money to buy failed talents, they will be stuck with them for many years and as a result have less wiggle room to make new transfers. (most leagues have a 25-man squad limit).
And Chelsea has a long history of making expensive failed purchases (like e.g. Lukaku, and he wasn't even a Todd Boehly purchase by the way).
Very ironic that nobody in the news is talking about that.