Only way it would go to VS upon AP engagement is if the takeoff was without using the flight directors. If you take off with the FDs on, and engage the AP at 500' you will be in TOGA mode, not VS.
To accelerate you bug the speed up. Use of VS instead of that will allow the A/T to reduce power from TO thrust which is not what you want in an engine out situation.
Vertical speed is seldom used in jets. About the only time is if ATC gives you a small altitude change like 1000 or 2000 feet and you don't want it to go the climb thrust for a small climb. Also used on non precision (dive and drive) approaches to descend to MDA.
Use of VS in most transport jets will have the airplane attempt to maintain the VS at the expense of maintaining speed. Not a good thing.
Most climbs you want to climb at climb power and a certain speed, Level change (737) Flight Level Change (757, 767) or Open Climb (A 320) will give you climb thrust and use pitch to maintain the selected speed. VS will maintain the selected airspeed. If below what can be acheived at climb thrust, it will be at reduce thrust and selecet speed. If the VS exceeds the climb rate the aircraft can achieve at climb thrust limit, it will trade airspeed in an attempt to maintain the VS, NOT a desirable thing.