Was Lt. Dmitri the father of Catherine's son?

Catherine, who is in love with Count Alexei, throws a locket with his photo in it out the window. A moment later, she runs into the garden to search for it. She encounters a young lieutenant out in the dark. They make love. It is, obviously, the young lieutenant's son she later bears.

Later in the film, she visits Count Alexei's favorite regiment. She talks to a young lieutenant named Lt. Dmitri. She looks at him with a knowing look and the dialogue is full of double (and suggestive) meanings. Was Lt. Dmitri the man she met in the garden who fathered her child?