Are ties possible?

As it happens...

A Lv80 Magikarp caps out at 1,986,589,014 JP. source
The 5th Magikarp in the Expert 1 League has... 1,986,589,014 JP. source

My Magikarp did not receive a cheer from the support Pokémon, so it should have been a tie. Despite this, the result was:

Springboard: 174.85m
Koylee: 174.84m

In the event of a tie, the player wins. Additionally, the "JP => jump height" formula seems to include a bit where if the result would be identical to the opponent, it increments the winner by one in the least significant digit.

I then got two 25% and a 5% cheer in a row so I wasn't able to get any more data out of Springboard. On to the next Magikarp:

Thanks to the ability to skip previously won battles, I was able to avoid the chance of cheers and this is what the 4th-6th battles gave:

Bouncycastle: 174.84m
Magikarp: 171.37m

Bouncycastle: 174.85m
Koylee: 174.84m

Bouncycastle: 174.84m
Magikarp: 175.53m

This conclusively proves that the game will inflate the score of the winning Magikarp if they would otherwise appear equal, and that ties are resolved in the player's favour.