How strong is the remote lockout on rock shox?
First, you should understand how suspensions with lockouts work. Fluid suspensions(oil or air) like yours have a valve inside them that lets the fluid flow through at a constricted rate on the way up, and very quickly on the way down. This is what gives the dampening effect on suspensions. Lockouts effectively completely close off that valve.
However, obviously the valve is not infinitely strong. At some point, it will give way and let the air through. This is where blow-offs come in. Blow-off basically refers to that point where the lockout 'fails' and dampens the shock anyway.
The model you have has something called TurnKey which is Rock Shox patented name for blow-off. It has an adjustable blow-off point which will let you set the amount of force required for the blow-off to occur.
Now that you know how these systems work, consider your case of riding your MTB as a BMX on a track. If you set the turnkey/blowoff too low, you'll risk it suddenly dropping on a big landing and if you are taking a turn or something immediately after, you can risk losing your balance. If you set it too high, you probably can damage the valve in the shocks by stressing it too much.
So to conclude, not really, riding on the lockout won't affect the suspension too much because as soon as the wheel hits something too hard, the lockout will 'fail' and go back to normal damping as long as you don't set the blow-off so high that it is practically impossible to hit the bow-off. Just don't set it so low you hit the drop-off all the time and defeat the point of locking out.