Considering that almost all weapons (That is, anything not a pistol) are typically held with both hands, it's kind of silly to drop the weapon with both hands when only one is injured. If you were injured in both hands at once, maybe (And still only maybe), or if it were held in only one hand (Pistol only, unless you want to count longarms during the German sprint animation). It's made slightly worse by the visual location of dropped weapons being entirely client-side, while pick-up range is server side, making it so you sometimes can't pick up a weapon (Sometimes you have to fidget around until you get in-range, sometimes it's completely impossible). And then you'd either have to drop the weapon with its ammo (Which is silly, but little more than the current pickup system), or re-code the ammo system to make weapon and ammo independent (A lot of work for such a minor and rare feature, but one that could at least be used as a framework for other eventual improvements).
So basically, I would say no. If the other features that would be needed for it have been implemented (Improved checking for weapon pickups and seperate weapon/ammo tracking), and there has been enough improvement to the injury system that it doesn't seem to be such an outlier, then it might be worth throwing in as well.
As for weapon damage, that might work. I'd be cautious about it if there weren't a full weapon reliability/condition system (Since otherwise it would be just a binary perfect/destroyed state), but if it were, that might work. To tell the truth, it probably wouldn't be worth adding unless the game made a significant push towards simulation. Again, it's a fairly rare event compared to some much more core elements that would need addressing first.