Yes, Miranda does fall in love with Ferdinand. Prospero's rough treatment of him as well as his own attractiveness moves her immediately to sympathy:
Is the third man that e'er I saw, the first
That e'er I sigh'd for: pity move my father
To be inclined my way!
Unlike the spirit Ariel or the half-bestial Caliban or her father, Ferdinand is handsome, gracious, and deserving of a young woman's interest. His exclamation to her that he will make her queen of Naples indicates a mutual affection such as one expects to find in the earlier romantic comedies.
Prospero's plan is to create an element of struggle for the young lovers so that they will more highly value the love he has conspired them to feel. It may seem that Prospero is the puppet master in this regard, but while he may arrange for them to meet, their love is authentic.