Can Han people add a dot in the middle of their household registration names, just like the dots for ethnic minorities and foreigners?

No such situation.

Even the name of a foreigner is written in a foreign language without any dots. The dots are added when writing Chinese.

For example, English is written one by one. Words are disconnected and cannot be misread. Chinese characters are not good. The characters are coherent. If you don’t add dots, they will be misread.