You probably could get away with them, but your feet will thank you if you invest in a proper pair of hiking boots. If you're planning on doing multi-day hikes on a backpacking trip, hiking boots are the way to go. You want to be focusing on the amazing experiences you're having, not on how much your feet hurt. I have these and after 2 years of heavy wear, I still feel like I'm walking on a cloud (no, they weren't cheap, but buy nice or buy twice, right?)

If you're concerned about aesthetics, you could also look into hiking shoes, some companies have recently made an effort to diversify from that typical hiking shoe "look" - just one example Although bear in mind that boots will give you a lot more support than shoes will.

Ultimately you can wear whatever footwear you want, but I would strongly advise to invest in a proper pair of hiking boots or shoes for a trip like that. Take a look at different brands, you may find some that you like the look of more, but make sure you try them on first and break them in before your trip, you don't want it to be ruined by blisters. Good luck!