VPI,
The short answer to your question is no, there is of course (inevitably) a rather longer one.
BEST ANGLE OF CLIMB
Excess thrust is thrust minus drag. The maximum attainable angle of climb is proportional to the excess thrust divided by the weight. So maximum angle of climb occurs at the speed at which excess thrust is greatest.
For both jet and prop aircraft the total drag curve is typically a bucket shape with the minimum value at VMD.
Thrust in a propeller aircraft drops off quite quickly due to decreasing propeller efficiency as speed increases. So the greatest excess thrust and hence best angle of climb occurs at quite a low speed. Strictly speaking this is at the lowest safe flying speed but a slightly higher speed is usually recommended.
In a low bypass (or no bypass) jet the thrust stays almost constant as speed increases. This is because increasing thrust due to ram effect compensates for decreasing thrust due to momentum drag. The overall effect is that thrust typically falls off as speed increases, levels off at about 250 Kts then increases at higher speeds. The actual figures obviously vary with engine type. So with almost constant thrust, the greatest excess thrust and hence best angle of climb occurs at the minimum drag speed VMD.
MAXIMUM RATE OF CLIMB
Maximum attainable rate of climb is equal to excess power divided by weight. So maximum rate of climb occurs at the speed at which excess power is greatest.
Excess power is power available minus power required. Power available is thrust multiplied by TAS. Power required is drag multiplied by TAS. For both jets and props the power required is rather like the drag curve, but somewhat steeper at the high speed end.
In propeller aircraft the thrust falls off rapidly with speed as TAS increases. So multiplying the two together gives a curve rising from zero at zero TAS, reaching a maximum at a fairly low TAS, then decreasing at higher speeds. So the best excess thrust and best ROC occurs somewhere close to ( but not actually at) the top of the power available curve.
For a jet the thrust is almost constant, so multiplying this with increasing TAS gives an almost linear increase in power available, as speed increases.
If you examine a typical power available/power required diagram you will see that the best rate of climb speed for a jet is much higher than that for a prop. Ram effect is proportional to the square of the TAS. So although a turbo-prop will benefit from some ram effect, its much lower speed means that this benefit will not be as great as that affecting a jet. With very advanced (high speed) propeller aircraft this gap will of course be narrower.
Such a diagram will also illustrate why your P3 climbs quite well at 30 Kts above the recommended best climb speed. The power available and power required curves are pretty well parallel close to the best climb speed. So you can deviate from it a little bit without losing too much ROC. If you look now at the curves for a jet, the situation is even better. Because the power available curve is almost straight. You can achieve something very close to the best ROC over quite a wide speed range.
(I tried to paste a diagram into this message but it got lost along the way)