They may wonder how you're going to fund the trip.
But here's some advice. I'd say, forget what med schools think. A round-the-world trip is a once in a lifetime experience, that you will think back to for the rest of you life. Do it if it's what you want to do, and you can make it work financially and time wise. Don't let applying to med schools get in the way of the life experiences you want to gain. It's not worth it. You'll figure out how to present the experience to med schools in due time.
That said, I would not recommend the trip if it overlaps with interviews. Or rather, I would not recommend applying this cycle if you will be abroad this Oct-Feb or so. Take the trip and work applying to med schools around it, and take an extra gap year if necessary. You will most likely not have time to take a trip like this again--especially in your youth.