I think "evil" is a very strong word to use in most contexts.
So on that basis, no beauty contests aren't evil. If we want "evil" to have any meaning beyond "dislikeable" I don't think many of the even the most ardent opponents to beauty contests would consider them evil.
But removing "evil" and looking at it in more general terms?
I don't particularly like beauty contests. At their simplest they are basically just an exercise in objectification. Even ones that try to be more nuanced such as the infamous Miss World still present a rather outdated view on what it means to be the "perfect woman". Even if we ignore the bikini and evening dress rounds, what's left? How much charity work you do (Beauty with a Purpose)? How fit you keep yourself (Miss World Sports)? How well you can sing or play a musical instrument (Miss World Talent)? How nice your Facebook page is (Miss Multimedia)? How demure and graceful you can be (Personality)? Is that really summing up the "perfect woman"? One who looks good in an evening dress and bikini, can sing a bit, has a non-controversial personality, occasionally shows up to Charity event and has a helper set up a good website?
But are they bad?
I can understand the arguments that by putting forward an outdated, somewhat masculine-centred view of the perfect woman these contests influence women to be that and nothing more. But I think that argument lacks strength for the simple reason that Miss World and similar contests are largely a piece of historical flotsam in today's popular culture. Sure, everyone's heard of Miss World... but could you name all the rounds in it (I couldn't... I needed to google it). Could you name the last five winners without resorting to google? If not their names then which country they're from? Hell, which continent? I couldn't and I doubt many could. Wait for Miss World later this year... I'll be you there will be far more coverage in the media about people complaining about it then about the contest itself.
As for the more brunt bikini contests and the like... I doubt there's any girl in world who's working away because her ambition in life is to be Miss Spring Break 2017. I'm pretty certain that most of the people who take part (willingly remember) do the contest, take a couple of shots, have a party and go back to doing whatever it was they were hoping to do before.
Many men like looking at pretty women, be they fully clothed, with a wet t-shirt, in a bikini or in even less. That won't change. And there are women who are willing... be it for money, popularity or because it makes them feel good... to put themselves on display. I may find the pretentiousness of Miss World nauseous and the crude howling of a frat pack at a bikini contest pathetic but I don't think there's too much particularly wrong about it.
I do think there are issues with child pageants and the like... although beyond the sexualisation of children a lot of my issues there are with parental pressure, as opposed to the events themselves... many of the same criticisms could apply to the "Tiger Mums" who put huge pressure on their children to be "perfect" in school and extra-curricular activities.