Yes, some can, which is why I said there is wide variation within those groupings. For example, some North Africans and West Africans can grow some pretty impressive beards, whereas I think the Bushmen don't grow any, and some Africans and people of African descent are in-between, with tiny or scraggly beards--but I'm not exactly expert on beards, so feel free to correct me if I err.
A complicating factor is the effect of diet. For example, vegetarian diets tend to inhibit hair growth in some people (my chest hair didn't grow hardly at all until I severely cut back on the plant foods in my diet, for example), so diet and other factors can add to the variations within groups.
On the other hand, the most impressive beards I can think of are the beards of the Persians in ancient times, and I'm pretty sure they ate plentiful grains and other plant foods, so one's inheritance seems to be the biggest factor in beards.