Can we testify that a man is a believer if he regularly attends prayers in the mosque?

Yes, there is no doubt that with the one who attends prayers in the mosque, his attendance is a sign of his faith, because the only thing that is making him leave his house and take the trouble to walk to the mosque is his faith in Allaah. 

With regard to the questioner’s words, “as it says in the hadeeth,” this is referring to the report narrated from the Prophet (peace and blessings of Allaah be upon him): “When you see a man regularly coming to the mosque, bear witness that he is a believer.” But this hadeeth is da’eef and is not a saheeh report from the Prophet (peace and blessings of Allaah be upon him).