Yes, the velocity will increase, BUT...you will likely run into pressure problems. Possibly catastrophic pressure problems. Steel shot requires diferent loadings with different wads because steel does not compress like lead shot does. Upon firing the lead shot will deform against each other (slightly) allowing a smooth pressure curve. The steel shot will not have that effect and pressures can spike to dangerous levels.
"Playing" with loads like you are planning on can and likely will end very badly for both you and your favorite shotgun.
Steel shot (BB's) may yield high initial velocity but will lose velocity more rapidly down range and does not penetrate as deep as dense material like lead. You will probably end up with most of the damage to you and your gun.