Yeah, the Page of Cups can absolutely read like a crush. The Knight, Queen, and King of Cups usually come across as deeper, more experienced or committed feelings. The Page feels more tentative, dreamy, shy-like someone who's smitten but nervous, maybe blushing, daydreaming, or wanting to send a cute message.
Think high-school crush energy: wide-eyed, hopeful, maybe a little awkward. It can also mean a younger or emotionally inexperienced person, a flirtatious note or creative gesture, or the very first stirring of attraction before it grows into something more. Context matters though - surrounding cards and court-card pairings will help tell whether it stays crushy or develops into something more.