if Cohen’s today are tamai, are their blessings still allowed and purposeful in the eyes of Hashem?

Shalom, Thank you for your question. You are correct in assuming that the full holiness of the Cohen is blocked today because of the level of spiritual impurity that exists. Until the Temple is rebuilt and we can return the Cohen to his service (as we pray for in the festival prayers), we will lack the fullness of Hashem's blessings. None the less, even today there is a mitzvah for the Cohen to bless us, and this is not dependant on his being pure or not. The Priestly blessing is a command that exist independently of the Temple. So, not only is this blessing allowed – it is an obligation for the Cohen to bless the people. From your question and our answer we can see a wonderful thing – that although Hashem clearly desires us to be on the highest level of purity and holiness, He none the less also wishes to bestow His blessings upon us no matter what our level be. In other words – Hashem stays with the Jewish people, constantly blessing us, through all stages of our being. May we merit for the rebuilding of the Temple and to be blessed by the Cohen from the Temple court.