Praise be to Allah.
If a person does not pronounce the Shahaadatayn and enter Islaam, we cannot say that he is a Muslim, even if he admired Islaam and recognized that it the best religion, a great religion, and so on. Abu Taalib, the uncle of the Prophet (peace and blessings of Allaah be upon him) died a kaafir, and Allaah forbade His Prophet to pray for forgiveness for him, even though he used to defend the Prophet (peace and blessings of Allaah be upon him) and said in his poems:
"I do know that the religion of Muhammad is better than all other religions of mankind;
were it not for fear of blame or slander, you would find me accepting it completely."
If a person accepts Islaam out of conviction, and begins to practise it, then he is a Muslim, even if he does not register his Islaam officially, or go to a court or Islaamic centre to obtain documentation, or announce it to others. If such a person dies, then we hope for Paradise for him and pray for mercy for him.
And Allaah is the One Who sees all that His slaves do.