Is it normal for a search engine to react to such a redirect?

Question

Search Engine Optimization

There is a site, each user has his own link of the type *site.ru/user_id*
When the user simply enters site.ru/, without entering the id after the slash, there will be a check:
1) If the user is not authorized, then you need to transfer him to another *site-account.ru* domain for authorization to take place there. When authorization is successful, the user will be transferred to site.ru/user_id
2) If the user has already been authorized, he will be transferred immediately to his site.ru/user_id
That is, one service has 2 domain names. One domain name for the direct use of the service, another domain name for managing accounts and logins