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There are a lot of variance between an empty roller coaster and a full roller coaster that can affect this answer. But lets assume an ideal case where these variance are negligable, and we are only dealing with the basic property of energy conservation.
Then yes, a filled roller coaster will take longer. Assume that the roller coaster has an initial energy E (it does not matter how we attained it, for a matter of fact, lets just say a huge monster pushed the roller coaster). So by energy conservation, this is converted to kinetic energy. And the nonrelativistic relation is E = .5 m v^2, so a full roller coaster has more ppl, hence heavier the mass, thus slower the velocity, so longer it takes to arrive..
Then yes, a filled roller coaster will take longer. Assume that the roller coaster has an initial energy E (it does not matter how we attained it, for a matter of fact, lets just say a huge monster pushed the roller coaster). So by energy conservation, this is converted to kinetic energy. And the nonrelativistic relation is E = .5 m v^2, so a full roller coaster has more ppl, hence heavier the mass, thus slower the velocity, so longer it takes to arrive..