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, shyβlike 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 β surrounding cards and court-card pairings will help tell whether it stays crushy or develops into something more.