IMO, not really... your scenario is the sort of a thing I imagine presenting to a student and asking to analyze. There's actually a lot going on if you
want to break it down into the individual parts, but the main feature of your example is simply gravitational potential energy -- a bigger hammer means more energy input from that source -- especially with a classic hammer stroke where the human just guides the hammer and let's gravity do the work.
In fact, it's quite difficult to talk about the force (in the sense of physics) with which the hammer strikes the nail, since it depends very, very much upon the duration of the impact of the hammer with the nail*. When a layperson would ask "what is the force (in the sense of English) with which the hammer strikes the nail?" they really mean something more like "momentum" or "energy" or "impulse" (those words meant in the sense of physics).
*: and possibly on material properties of hammerheads, nails, and boards, to control whether the force is essentially constant for the duration of the impact, or if it varies
(I'm 99% sure of the following physical claims)
If you were swinging the hammer horizontally (i.e. the hammer remains horizontally level for the entire stroke), you might be surprised to find that the size of the hammer doesn't actually have any direct effect on your ability to drive the nail. A bigger hammer can still help, but for the following reasons:
- The hammer accelerates more slowly, giving you a greater amount of time over which your muscles can supply energy
- The hammer moves more slowly for the same amount of energy, allowing you to swing it more safely
(that first point is actually a decent example of F=ma -- in particular the relationship of mass to acceleration when holding force constant)