A friend of mine says that the HP of your Pokemon will affect the catch rate (lowering your chances if your Pokemon has low HP). I'm fairly certain this isn't true, but wanted a second opinion.
The formula also takes into account the following factors: The health of the Pokémon (relative to its full health) The type of Poké Ball Any status condition of the wild Pokémon Any active Pass Powers (in Generation V), O-Powers (in Generation VI), or Rotom Powers (in Pokémon Ultra Sun and Ultra Moon) Certain other factors, such as the target Pokémon's level, may also factor in depending on the type of Poké Ball used or the generation.
The formula also takes into account the following factors:
The health of the Pokémon (relative to its full health) The type of Poké Ball Any status condition of the wild Pokémon Any active Pass Powers (in Generation V), O-Powers (in Generation VI), or Rotom Powers (in Pokémon Ultra Sun and Ultra Moon) Certain other factors, such as the target Pokémon's level, may also factor in depending on the type of Poké Ball used or the generation.
Source
A party Pokemon's HP doesn't affect the catch rate of a Pokemon.