I will focus on your main question in my reply. I would personally not recommend to use travelling as a main reason for joining a consulting firm for a couple of reasons.
First of all, joining consulting mainly for the travelling experience doesn't signal a good candidate. Although you should be willing to travel, they key elements of the consultant job are related to a love for analytical works, working in a team and face to face with clients, being intellectually curious, willing to learn about several different sectors and the desire to have an impact from young age on relevant companies. Yes, travelling could be something you enjoy, which makes you apt for the job (assuming you can show you already enjoyed the experience and it's not just an idea), but should not be the main reason for your choice - otherwise the interviewer may argue if you have a clear understanding of what the job involves.
Secondly, for many consultants, travelling for work is not a plus of the job (although the points for airlines and hotels come very handy for vacations). Actually, it can be a minus. This is not only true for people with families, but also earlier in the career, since, after the first excitement for travelling first class and in 5-star hotels, travelling makes more difficult to have a stable life with reliable routines (friends, gym, dinner with friends and relevant others, etc..).
Now, I remember that before joining consulting I was very attracted by travelling. But I also remember I was very happy to be based back in my hometown after 3 months spent moving around Europe breaking my daily routines.
Thus, unless you end being on of the few people that genuinely love travelling for work and have tried this before (and thus can backup this passion with actual work you have done abroad), the interviewer could consider such claim based on lack of experience, and wonder how you would react to the consulting environment once discovered that, in the end, travelling for work is not as good as you imagined.