Not a lawyer, but the chances of ABC being able to do anything are virtually nil for two reasons - (a) the ads only run for a couple weeks at most - it will take months or more for a lawsuit to wind its way through the system, and (b) there is no damage - the swifties aren't profiting and ABC isn't losing profits. There is virtually no way ABC could see a dime from the non-profit swifties, who will probably disband shortly after the election, giving their remaining bankroll to the RNC or charity.
The best that ABC could hope for is a court battle followed by an injunction to stop showing the footage--any "damages" would not be settled for years.
In all probability an injunction would take until after the election and the court battle would give the Swifties lots of free publicity.
I hope ABC pursues this.