TL;DR: The legal incompatibilities between the GPL and the App store TOS don't apply to the MPL, but there is no saying whether Apple will allow your MPL licensed app.
First off, what Apple allows and doesn't allow in their app store is entirely up to Apple. As far as I know, they reserve the right to refuse any app for any reason whatsoever. Therefore, it is impossible for us to guarantee that an app will not be rejected from the app store for it's license, whatever the license is.
As far as the GPL goes, you can't legally distribute GPL licensed apps through the app store, because the terms of service of the app store, and the GPL are incompatible. There are restrictions in the TOS of the app store on what you may and may not do with an app you receive from the app store. The GPL disallows any such restrictions in paragraph 3 of section 10:
You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. [...]
Therefore, it's impossible to simultaneously comply with the app store TOS and with the GPL.
The MPL doesn't have such a clause, implying that additional restrictions may be placed on an MPL licensed work. Assuming that the app store rejects GPL licenses based on the above rationale, that rationale wouldn't go for MPL licensed apps, and there would be no problem in distributing an MPL licensed work to the app store.
I, along with everybody else, have not read the TOS of the app store in its entirety. There may be other restrictions or reasons why legally distributing MPL licensed software through the app store impossible, but it seems unlikely.
Therefore, I consider it likely that Apple will allow an MPL licensed app in their app store. There is really only one way to find out if they do: try it out.