When the PC holds a shield in his left hand, and is hit by an enemy attacking from the right, does the shield still add to the PCs armor?
In general, I'd give the PC the use of the shield - "the orc charges you from the right, and you instinctively twist to get your shield up as he swings his hammer". This is because there's nothing explicit in the rules about the shield being dependent on positioning.
If earlier action gave the character a negative consequence (like establishing weakness, fatigue, or disability), or allowed you to make a GM move then sure, you could say "you're off balance and won't be able to bring the shield to bear against the orcs coming at you from the right."
As with a lot of the questions you're asking about Dungeon World, the answer here is 'it does if it makes sense within the fiction you have established so far'. A definitive yes or no is impossible, because it depends so much on the individual circumstances within whatever scene the question is being asked about.
So, you need to ask yourself - does it make sense in this particular scene and these circumstances for the shield the character is carrying to add to the armour of the character, making them more difficult to harm? If the answer is yes, then the shield should add to the character's armour. If no, it shouldn't.