They will - the key part is "no association can have more than four teams playing in the Champions League" - if one of the top four (or more like two or three of the current top four) failed the FFP test then the places would drop down the league until you got the four spots filled.
Also I think the team with most to fear is the ****e - they have lost around £40 million each of the last couple of years, and given how much Rodgers has spent are certainly facing a similar loss this time around. Also, Yanks II also havent really invested anything in youth development, infrastructure or done any of the crazy things that City have done to try and disguise spending.
It will be interesting to see what happens if an English side win the Europa and a team outside the top 4 win the champions league. Top 2 for champions league only?