Yes. With the understanding that the wound has some mechanical impact, where the hit point loss (if it doesn't kill you) doesn't have any impact. It should be a trade off.
Balancing this would be really difficult, though.
As a DM-added, DM-arbitrated rule in 5e, I don't think balance would be a big consideration. A DM instituting such a thing would find his own balance that works for his campaign pacing, just as he finds a balance in encounter difficulty and spotlight time for the same. If it's worth complaining about D&Ds lack of realism or modeling when it comes to serious wounds and natural healing, and worth messing with the rather delicate balance among encounters/day, healing/day, and other daily and short-rest recharges, then it could certainly be well worthwhile.
It could be presented to the player as a choice, arbitrated by the DM, or based on numbers:
A) Numbers: when you are critically hit or hit for a threshold amount (say half your hps in one blow), you take a wound with mechanical effects instead of the full damage. (So, it would replace the extra damage from critical hits, and could reduce massive damage by, say, half).
B) DM: arbitrated: when the DM feels like it, he rules that the character takes a wound, either instead of or in addition to loss of hps.
C) IC decision: When the character would be dropped by an attack, he can instead choose to fight on out of sheer determination. This 'opens' the wound he just took, making it much more serious, but he retains his hps.
D) Player arbitrated: When player decides it'd be dramatically or tactically appropriate, he chooses for his character to take a wound instead of hp damage. This can be at any time the character takes hp damage.
Balancing the mechanical penalties of the wound against the hps retained shouldn't be too hard.
Then you'd also need a system for tracking and recovering from wounds.