Yes, it seems this is what draws Emma in, the intrigue of it all, filling out the blank canvas of Harriet to suit herself. Emma would be at a loss for what to do, with the absence of Miss Taylor, her despair at lonesome evenings with her father, not daring to walk far beyond the house, etc. Her loyalty to her father seems to dictate what she does.

Emma says she would have immediately asked who her parents were, if she was in Harriet's situation. She says Harriet had "no penetration", so she seeks to "help" her in a charitable fashion.

But rather than being motivated by a genuine compassion for Harriet's situation, IMO, Emma takes on her case for it's intrigue and how it will employ her fixed role of being "useful". It seems very mechanical to me, impulsive to fill a vacant space and relieve her of despairing of solitary evenings at home once her father has retired.