Is it possible to estimate range / distance ( within reason ) just by using your parallax dial on the scope ?
No.
there is varying degrees of accuracy to hit the target. If you're shooting a relatively fast cartridge, something 2700 fps or more for example, you're going to be within some type of max PBR. Especially if the target is larger.
Around 600 yards, atmospherics and BC start to really come into effect.
Most paralax adjustments aren't that accurate to begin with. Even on more expensive scopes. Some brands don't even put yardage. It's just a quick reference, and then you check for reticle swim and actually dial the paralax.
It's a legacy skill. It doesn't make much sense anymore, but using a reticle is going to be the way to "estimate" range without a rangefinder. The more accurate you read the measurement, and the more accurate you have a size of the object you're measuring, the more accurate said estimation will be.
I already know someone is going to reply to me and tell me how they use mil estimation/mildot master etc all the time in the field. First, I don't care. Just because you do it doesn't mean it's more accurate than laser. It's certainly not faster.
Distance = (Target Size x 1000) / Mils