Sort of. Like the "Dead" status of Spinarak, the Pokemon will do something. It could "Run away frantically," "Dig into the ground," etc.
You must note if the RP'er had the chance to try again.
But after the second time, if they fail, the pokemon is now permanetly uncatchable.
After an RP'er has success/failure, they can't catch another Pokemon on that route. That's why Fisherman Tully's quest is a sorta tough choice. You can get the prize and pass up catching a Magikarp, Tentacool, or Corsola, or try your luck.