Short answer: no, a little fat-free food isn't going to harm him. There doesn't need to be fat in every morsel he consumes, as long as he's getting enough healthy fat - enough healthy calories, period! - from his other food. But....
....there's a longer and more complex answer that isn't so simple when planning long-term for meals and snacks and so on.
In general, "fat free" foods aren't necessarily good for any of us. We, and that includes adults,
need to have fats in our diet. The caveat is that they have to be "good fats" or they do more harm than good.
A lot of food specifically marketed as "fat free" for adults isn't all that good for us. There's a difference between naturally free of fats and oils, like a carrot, for example, and more processed foods where the fats/oils are replaced with other things, usually carbs and chemicals and other empty calories. In addition, fat-free foods tend to be the least filling in the long run, so while one might feel completely stuffed after a meal of pasta or rice without any fats or oils, it's less time till one is hungry again, whereas a meal with good fats makes you feel full longer and you can end up consuming fewer net calories overall. I lost more weight ADDING coconut milk and oil to my diet - and consuming full-fat dairy - partly because I just wasn't hungry again in an hour or two; I could make, say, a smoothie with full-fat yogurt and coconut milk and whatever else I wanted in it and it would keep me full for 3 hours no problem. (I also took out all grain and legume products, so it wasn't just the addition of the good fats, but adding in the fats to replace the grains was surprisingly filling.)
There's also a big difference among kinds of fats: omega-3's vs omega-6's, for example, and saturated vs unsaturated fats. Omega 3's and sat fats are the healthier options in the long run, assuming not consumed to excess and assuming the sat fats are NOT hydrogenated oils. Omega 6's are more plentiful and it's easy to get too many of them, AND in excess they are inflammatory - and they're found in most available vegetable oils: corn oil, soybean oil, canola oil, and sunflower - the nuts and seeds, mostly.
Vegetables are by and large fat-free and of course they're fine to give to pretty much anybody.
They're nutrient-dense and many of them deliver even more nutrition when accompanied by some animal fat, like butter, tallow, lard (for those who eat pork), or chicken or duck fat; coconut oil isn't animal-based but it's another good choice, and olive oil is a great healthy oil as well.
So absolutely let him have a bite here and there of whatever you're eating as long as it's healthy calories overall. If he's ever asking for fat-free commercially-available stuff where the fat's been replaced by chemicals (can you believe that here in the States we have fat-free sour cream?
), though, I'd take a pass on it.
More about fats and oils here:
Saturated fats can be GOOD for you! (just not trans fats)
