Nonviable is subjective. I'd play them, and they would be sickley as all get out.
Well, that depends on the edition.
First off, in 1e if your Constitution is a 3, you can only be an Illusionist (assuming you rolled the 15 int and 16 Dex I guess? If not you're absolutely non-legal for play). So enjoy your human illusionist (you don't meet the requirements for any demihumans). Your hp is 1d4-2 per level.
2e will get rid of that pesky "you can only be an Illusionist" rule, so my suggestion is to play a fighter and pick a longbow. 1d10-2 is your best hope for survival.
Basic is actually even more brutal: Con penalty for a 3 is -3, and HD for classes is smaller. As a magic user or thief, you can only get 1 HP per level and as a fighter, 1d8-3. Good luck!
3e makes the penalty even harsher: -4 to hp, fort saves and concentration. At least races and classes are uncapped so my suggestion is be a dwarf (5 Con/-3 penalty). I'd suggest grabbing a level of barbarian for that d12 HD and temp Con boost, but you could only rage for 2 rounds (1 if not a dwarf) before beginning fatigued.
So realistically, your character is not surviving any sort of hit from any creature. The best you can hope for is a good way to become hidden and just soak up XP while your allies do all the work. Any class but a fighter type means your ho is basically 1 per level average (the minimum). You might survive for a while if you are a coward, but I don't give any character with a 3 Con a real chance of surviving. This is suicide played out for extended effect.
So, yeah. Not viable unless you want to be one of those baker dwarves.