Nope.

The thermal paste when overly used (in quantity) will decrease it's efficiency (thermal conductivity) by a lot.

You can replace the thermal paste/grease the factory HSF has by cleaning the surface and then applying your own paste/grease, but DO NOT add more to what it already has.

Also, always apply a small amount to the CPU surface cause the same rule applies: an overdose will work against the idea of improving thermal conductivity.

Cheers!
 
It should be better, yeah.

Just read the instructions carefully and watch some videos on how to apply the thermal compound efficiently across the CPU surface. That is, if you don't know how to do it.

I usually do the "apply and spread". Clean the surface of the CPU (if its dirty with human grease or dirt) and be careful about not touching it directly with your hands at any time. Then, apply one "drop" (it's not liquid; watch a video for this) of thermal compound in the middle of the CPU and then spread it with something like a ruler over the surface leaving a very thin cover and no visible area without thermal compound.

Cheers!