Can a goy who wants to become a ger enter a non-Jewish place of worship for secular purposes (to get a paycheck from someone who is there) and then immediately leave?

If it is a place of worship which has idols, then the non Jew may should not enter into the sanctuary itself, but may enter the offices in the building or an adjoining room. In a situation where there is no other option a Rabbi should be consulted. If there are no idols, (Baptist, for instance) there is no problem.