No, it's not necessary (though perhaps desirable) but you'll have to get a third party app like Clipwrap and turn mts files into .mov files if you want to follow a Compressor-only workflow. Otherwise, copy the entire card structure and bring that into FCP or some other editor.
Not to second-guess, but I doubt you'll be happy with the results if you rely solely on Compressor – particularly since you indicate you care about the audio quality. Inevitably you'll want to correct something in post other than settinng in and out points…whether you do that in a video or audio editor.
Finally, remember that Vimeo is going to re-compress whatever you give it so be careful not to too aggressive in making your compression settings.
Thank you, Russ, for taking time to answer my question, which leads me to another question: Given the video clips are destined for Vimeo, does FCPX have enough compression/conversion capability to generate a video file (medium quality 640x360 video, high quality audio) for Vimeo upload, thereby avoiding the need for a Compressor 4 step? It would be nice to have to rely on a single app to ingest the AVCHD clips and generate a file ready for Vimeo upload. Thanks again ...