The answer is definitely yes. The preference for using one hand to another is generally tempered by other activities of skill in these modern times. It is now more common than ever to find left-handed individuals being able to perform right-handed activities, as you say your step-son can play right handed drums.
I myself was a right-handed guitar (Hendrix) beginner when I was 10 years old and I forced myself to play guitar on the left - my dominant hand (right) thus becoming the strumming hand. This was not natural for about 3 months but again, the through practice and conditioning, like all skills, this can be acquired.
The reason I will put forward for the dominant hand being the strumming hand is due to rhythm and your possession or control of it. Ambidexterity (which is rare in guitarists) is where a player has cross-dominance of either hand. This means that you essentially do not have a MUSCULAR PREFERENCE. But most of us do not have cross-dominance - but prefer a side. In fact, humans as a species tend to be more right-handed. Some studies indicate that this right-handedness has something to do with the right hand's (and the brain's) ability to interpret and perform rhythmic patterns.
HAND PREFERENCE CONSISTENCY AND SIMPLE RHYTHMIC BIMANUAL COORDINATION IN PRESCHOOL CHILDREN
READ THE ABSTRACT
I'm not a neuroscientist, but it's interesting to note that the DOMINANT hand has been observed to be able to carry a constant and "faster" beat. ie. 16ths notes as opposed to 1/4 th notes: similar to a drum pattern for a standard drummer where the high-hat is tapped by the right hand and the "slower" beat is kept by the left.
So, the guitar without the fretting, is essentially a rhythm instrument. The strumming hand needs to perform a skilled task of keeping time and being dextrous to also be able to accent individual notes/strings. This is similar to the drummer analogy above. This preference is innate and "natural" - similar to tapping your hands against your hips, one keeps a fast beat the other keeps a slow beat but both in time - which hand do you prefer for the faster/slower? This simple test should be a good indicator of which end your guitar will go.
Most people focus solely on the fretting hand as being the driving factor in determining guitar "sides". I think this is really a judgement of comfort between the jobs that the two hands need to perform: If there is a natural order to strike the strings instead of intricate finger-work you will quickly see this and that should determine whether you are left/right handed.