Will visual acuity always determine eyeglass prescription?

No, not always: Visual acuity is a measure of how well you see. In most cases this reflects on what your prescription might be but it can't estimate it exactly. There are many other factors that determine how well you see: if your retina is healthy and if there are other problems with your cornea or lens. It's possible to have poor visual acuity and yet have no need for glasses.