Only if we do away with gerrymandering, which is never going to happen. Gerrymandered districts are one reason that Congressional incumbents are re-elected at such a high rate (and, therefore, that once a party takes control of the House, that party tends to stay in control for at least a few cycles). Likewise, awarding electoral votes by CD may make it more difficult to vote out an incumbent President.
Also, especially given the gerrymandered districts that exist, this method would make it extremely likely that the party in the White House would nearly always also control the House.
Even though this approach would likely benefit the GOP in the short term, in the long term, I think it would be bad for the country.
The White House has nothing to do with redistricting in the states. Who controls the state legislature controls the gerrymandering.