I did the reverse and it worked out fine so no reason you shouldn't get the mileage bonuses.

That being said, I wouldn't just blindly cancel the MileagePlus Club card - it's one of the best general spending cards out there at 1.5 miles per $ of general spend. There are so many categories of spending that will never get a bonus on cards like Freedom (or SP or Ink).

The benefits - lounge access, Hyatt Platinum, priority security/check-in/boarding/baggage claim, Avis Presidential Plus, etc. are quite valuable for those who are on the road a lot.