Sure. But knowing that everything you do fails and you suck does not endear a player to his character, nor does it make him want to keep playing.
This is great for dealing with constant bad luck, but less so for swingyness. For that you need to replace the d20 with 2d10 or 3d6... but that can have very big repercussions, so it's not a step to take lightly.I had a friend who used to play with what he called a Deck 20. Basically 1-10 of 2 suits of playing cards with a Joker to act as a reshuffle. One suit was the 11-20.
Reduced the randomness considerably.
Lorenn searches for a whip and helps his friends to find motivation.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.