Hi,
When you use the "simplified registration", HikaShop will create a Joomla user and will sent the user password by email.
If the user does not have his email, he won't have his password to log-in and won't be able to see his orders in the HikaShop front-end dashboard.
But otherwise, if you can see the order in the backend, the corresponding user will be able to see it in the front-end.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.