Well, statistically speaking, I think that those people who are taller, with symmetric visages, higher hormone levels and more pronounced sexual features are considered more attractive, and that those factors also have a statistically significant positive correlation with career success. Something to do with people subconciously selecting partners on the basis of genetic fitness, but probably also down to some degree of people actively hiring and promoting subordinates they'd like and think they can coerce into sleeping with.
This could mean that your looks are likely to affect your chances at interview. However any statistical link is only partial (a small factor among many others) and it certainly doesn't mean that it'll be an active factor in your particular case.
There are some people (not just talking about consultants here) who will be more judgmental about your appearance than others. There is a case for good looks in terms of being more presentable and acceptable to clients, but sales is only one part of a consulting job and you're (hopefully) not going to be selling on the basis of the client wanting to get into your pants. There is also a case for being healthy and fit (an issue that's distinct from your looks in my mind): Consulting involves hard work and travel on minimal sleep and stamina's pretty important.
There are also people who won't be as bothered about looks, or who have different views to you about what beauty is. Consultants tend to be more educated and aware of their own prejudices. Some people may also be more ready to hire people they don't perceive as threats. I once worked with a (female) partner who would only hire men and "plain" women. Anecdotally, there are lots of consultants with terrible teeth and haircuts (I blame it on never having time to go to the dentist and using too much cheap hotel shampoo). At the extreme end, if you are "ugly" to the point of disfigurement or speech impediment, a lot of people are trained to over-ride their first impressions and apply a "disability allowance" when interviewing these days.
Finally, people who feel more attractive tend to reflect this in their demeanour. Confidence in conversation is likely to serve you well in an interview. So, worrying about your looks in the first place could be your only real problem - my advice: fer'gedda'boutit (there so should be a Goodfellas smiley on this forum).