Yes, but David didn't have the benefit of the revelation of the Father in the Son.
(CLV) Mt 22:41
Now, the Pharisees being gathered, Jesus inquires of them,
(CLV) Mt 22:42
saying, "What are you supposing concerning the Christ? Whose Son is He?" They are saying to Him, "David's."
(CLV) Mt 22:43
He is saying to them, "How, then, is David, in spirit, calling Him Lord, saying,
(CLV) Mt 22:44
`Said the Lord to my Lord, "Sit at My right, Till I should be placing Thine enemies" underneath "Thy feet"'?
(CLV) Mt 22:45
If, then, David is calling Him Lord, how is He his Son?"
(CLV) Mt 22:46
And not one was able to answer Him a word, neither dares anyone, from that day, inquire of Him any longer.