I'd say odds are better if you send by post, avoid DHL, FedEx etc. I got my laptop through no problem with USPO delivered by Thai Post. But it's always a gamble 🎲
I wouldn't pay for any treatment until after I got my Visa, what I would do would be to contact the orthodontist that you're dealing with, have them write out a treatment plan that explains it'll be a multi-year process that goes into detail about appointments and timings, have it stamped by them and submit that. Also likely good to submit some documentation about having some initial appointments booked.