No you don't. Besides, it's not that easy as registering for a us account (which btw you can login on with your non-us account). US prime actively checks for both US ip address AND USA billing address to show you US content
not quite so....
im in europe, and took u.s. prime trial,and it works fine. and they sure know my address is in europe.
your login credentials on amazon is the same on primevideo.com and on any international amazon site.. eg.. germany, uk, u.s. ...
you can pick the free 30 days prime trial also on all of them.... so i am now going on my 3rd free prime month ...
but to be able to view the u.s. content, your ip has to be in the u.s. (the british amazon site is the trickiest... it seems to notice the nordvpn u.k. servers,and tells me most of the time that i am not located in the u.k.,and asks me to disable vpn .. and therefore can not view any of the videos there,and tells me to head over to primevideo.com ... u.s. works well..)
edit:
it could be,if you only have the primevideo dot com subscription, that it might not work then. it's not the same as amazon prime membership (which does include primevideo ofcourse)
amazon u.s. does show on the web-page to me:
Based outside of the U.S.? Some titles might be unavailable in your current location. Go to PrimeVideo.com to see the video catalog available in <your_country_here>.
But I can view the videos with vpn.. (atleast with .u.s. prime trial membership..)