Not necessarily. Lenses are a complex formulation of curved pieces of glass whereas filters are single thin pieces of flat glass or resin and if made from high quality materials would not require the same type or number of coatings as a lens would. Of course, adding any extra elements (such as a filter) to the optical path will affect the way the lens resolves but this may not be so detrimental as to be visible in the final image. I think that multiple coatings are really there to add value to the filter for the manufacturer rather than for any highly useful purpose. I personally have never used multi-coated filters and have not found any detriment to my images. The multiple coatings should do no harm though so feel free to pay extra if you wish for peace of mind.