It depends on context. Pursuing a romantic interest can be just as positive as pursuing an interesting in learning to speak French. The word is neutral.

Pursue can be used in this way. I understand the meaning. It would be better to say young lady or young woman. It is a strong word for this situation. A male animal pursues a mate. The bull pursues a cow. A young man shows interest in a young woman. A young man is especially interested in a young woman. He likes her and is wanting to get her attention.