Can I propose to search for exoplanets or work upon exoplanet-related science?
No. Exoplanet and exo-planet related science is reserved for the Kepler Science Team. Furthermore, by proposing for Kepler GO targets, you are agreeing to the policy of non-disclosure of exoplanet information obtained serendipitously or otherwise through your GO targets. This policy is described in the NASA NRA and all GOs will sign non-disclosure agreements before receiving their data.