I don't know if and where there are Mellotron samples in Logic, but if you're really into these kind of sounds, I recommend looking into M-Tron Pro by gforcesoftware and SampleTron by IK Multimedia. I do think they both come as plugin AND stand alone versions and offer demos to try before you buy.
Of course you have to shall out some extra shekels, but if you really like these "instruments" and sounds, they're worth it, both IMO.
Best,
Claus