I subscribe to the "hit points and damage are abstract" philosophy. So my answer is, sometimes.
When a thunder bolt that pushes you off a 30 foot balcony, it is going to hurt. But you are so tough, it might merely knock the breath out of you. you take a moment to recompose yourself, and you're good to go.
A vine horror may be strangling you. By the time you get free of it, you have really exerted yourself, and perhaps need a short rest, but after that short rest, some superficial scratches around your neck are all that's showing.
You could be skewered by a spear, and taking ongoing 20 damage. That's a bleeder! Some magic might heal it, or you could be inspired to ignore that bleeder, but at the end of the fight, you'll have to tend to it. You will have lost a lot of blood, but probably carry around some magical healing, or liquid courage. But ongoing 20 damage could also be a dislocated shoulder. It hurts like Hades, but a heal check could pop it into place, easing the ongoing pain.
I leave PC injuries to the player's imagination. Some players like to imagine themselves walking in plate armor, their boots always filled to the brim with their blood after a battle. Some players like to keep their foppish attire immaculately clean through the goriest of battles. Same way with healers. If an eladrin warlord with an arcane background and multi-class insists that his healing is magical, I won't argue. It's all just flavor. Similarly if a warpriest feigns ignorance of any magic, and wants to do all his healing via inspiration, supplemented by herbs, that's fine too.
It's really all just flavor.