Math preparation is the single most important factor in getting an engineering degree. If the student has really masters AB Calculus, or better, all of BC calculus, then Calculus 2 and 3 will go easier. If in doubt, repeat the math!
I don’t agree that mechanical engineering is quite the same as four years of calculus, although many classes will use some calculus, algebra is also used in many mechanical engineering classes. Design principals classes will teach design for manufacturing for instance. Fluid flow and fluid dynamics classes are math heavy and thermodynamics contains partial differential equations but also has some easier math equations where solutions can be memorized so I think much easier than partial differential equations.
Engineering curriculums today include quite a bit of lab work and computer programming. So a student who already took JAVA or Pascal will be well prepared for GaTech or Clemson. It will be a lot of work to get an engineering degree at any of these schools.