While that is the case for many programs, it’s absolutely not the case for modern web browsers. For example, navigating to はじめよう.みんな¹ in Safari 9² and Firefox 46³ does show the IDN as it’s supposed to look to the end user in the address bar.
(Of course, internally, it’s still represented as an ASCII string (using Punycode⁴)).
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² — http://i.imgur.com/KX5i9aW.png