If we're talking scraped knee, or just a tumble, then no I wouldn't pick them up. I would get on their level and ask if they were okay, or if they wanted help up, or point to (or help find) mom.
But if it were a question of preventing an injury, absolutely I would catch/grab or what have you. And if it was a bad injury, then yes I would pick a small child up. My dd1 at 2, tripped and smacked her face on chair and busted the inside of her lip (it was a small, but deep gash that probably could have used a couple stiches.) I was across a fairly large room, but a mom who was just a step away from her grabed her in her arms and started rushing her over to me, and we met about halfway. At first I was a little surprised that someone I didn't really know would do that, but when I saw how much blood was coming out of her mouth I was really glad that she had done so. It was painful and scary enough that my dd needed instant comforting. And I will say that she calmed down really fast even though it was pretty bad, so I think it helped. So if it's an injury that makes me worried as a mom, then yes, I will pick up a LO if mom isn't right by.