I just heard that phones that aren't registered can't be used. Any truth?

yes this is total truth. phones are charged upto 16% on your original envoice with IMEi number . recently i send iphone to one of my relative and shw was charged around 14% plus unlock price . this makes authentic nepal buy phones alot cheaper

This is not true bro.
First, There was a proposed project from the Nepal government trying to impose a rule that unregistered phone that was not paid tax not gonna work, But currently, that project is on hold since they cannot implement the rule for each and every phone. Basically, the IT contract team there in Nepal failed in this project.

Secondly, as per the Nepal custom, the rule of carrying a phone is, you can carry one phone to Nepal and do not have to pay any tax for the first phone. But there are many cases ppl have taken multiple phones with themselves in hand-carry and custom ppl do not even bother to check anything unless you have a piece of bad luck, but you can take one phone without paying any taxes as per the custom rule and regulation.