A theoretically totally immersed blade would show no visible surface effects.
Thus, insofar as the penalties for immersion at the catch and the finish can be kept small, it seems to me that "digging deep" would not be a bad thing.
There are those who worry about the supposed drag resulting from that portion of the shaft buried with the blade. The shaft, near the blade, is merely an inefficient extension of the blade surface area itself -- contributing weak additional propulsion, perhaps, but no troublesome drag.
All other things being equal the larger the rower's effort on the blade the larger (the more energy dissipated in) the puddle. This is not to say that a larger puddle is (necessarily) less efficient than a smaller one. Of two rowers with blades of equal size, immersion, skill, and efficiency the stronger rower will inevitably leave the larger puddle - and will certainly be the faster.
Alternatively, all other things (including rower effort this time) being equal the blade and stroke with the higher efficiency would be expected to leave the smaller puddle.
Puddle size, by itself, is not a good indicator of anything.
A Simple Experiment:
Those handy among you set up the following simple experiment:
Arrange an oar (or blade only) on a fixed fulcrum (or support only) such that the blade may be set at a range of immersions at ninety degrees to and in a steady stream current of about 2.0 m/sec (a typical rowing attack [slip] velocity at the oarshaft ninety degree point).
Measure the force required to keep the blade in place at varying depths of immersion and take note of the vortices (puddles) thus produced.
My guess is that, up to a point, the resisting force will increase with immersion depth and that the vortices will seem less and less evident.
However, increased force with increased immersion is NOT what happens in rowing. The force at this point in the stroke (the result of the rower's effort at this point) is always the same - he doesn't change how hard he pulls - after all he's pulling as hard as he can. See Propulsive Force.
A Not So Simple Experiment:
Thus, the force must remain the same as immersion changes. What will change then is the slip (attack) velocity.
So now, with the same setup and for each discrete immersion let's change the stream (attack) velocity such that the force is always the same.
What happens? As immersion increases the required stream velocity (the blade slip) must decrease: a sure indicator of increased blade efficiency. As velocity decreases so, too, do the vortices.