Q: Will an aloe hybrid classified as small eventually grow big and tall?

A: The size classification in this website indicates the fully grown size of the variety. Consequently a "small" cultivar is bought very close to its fully grown size, "large" cultivars bought in a nursery bag will need a few years to become fully grown.
Refer to this article “a-guideline-to-our-plant-size-category” for more information.