Well, it is possible, but not generally a good idea.
You can easily disengage two gears, but there will be a jolt when you try to engage a moving gear with a stationary one. If the load is light and there is some elasticity in the chain, it could work. If the load is high, you are likely to damage the gears.
Normally gear changing with live systems uses a clutch, maybe a sprung coupling and in cars for example synchromesh cones - all trying to reduce the damage caused by crash gear changes.
The nearest I can think of to such a system, is a derailleur gear on bikes. There the chain engages with a gear moving relatively slower or faster rather than stationary. The difference in speed is not very great and good technique is to reduce the load during the change. I would guess this is your best option if you must have a live gear change without a clutch.
As far as energy loss is concerned, I think that would be very difficult to quantify. More to the point is, not how much energy is lost, but where that energy goes! Some will go into noise and heat, but some will probably go into bending and possibly breaking the mechanism. If there is no damage, I would expect the energy loss to be small (but then I do expect damage!)
If you use a clutch, the main energy loss is due to slip and would be quantifiable if you know the duration and torque profile of re-engagement. Essentially the slip loss power is torque x slip speed.