Absolutely. My two year old son now wears a pair of second-hand shoes bought in a boutique that also sells used children's clothing (but only high quality items). It fits him perfectly. Before that a pair of practically unworn shoes with LED-lights in the soles was worn a handful of times; it fitted right enough, but in the summer a pair of Tefa sandals was much more comfortable.
Some pairs of shoes see much more wear than others, and unlike adults, when kids don't wear a pair for a while because the weather is more suitable for other things (sandals or wellies) they'll often hit the next size up by the time they can wear them. So sometimes shoes will hardly be worn at all.
And a pair of kids wellies must see at least twenty pairs of feet before retiring. I don't think these actually ever get to the stage that they are worn out: they just get lost somewhere on the way long before that.
Because shoes tend to wear out a lot faster than other clothes plus wearing shoes that are broken in to someone else's foot doesn't tend to feel all that good.
As long as they seem to fit well it's probably fine, we have used both new and pre-used. But shoes form a bit after the users feet, and if they're used a lot (as shoes are as opposed to rotated clothes) they might be less comfortable and supportive than one would want, and kids depending on age aren't great at realizing they could do better.
If we get used shoes we
At least that's my experience and interpretation of my kids, but YMMV.