Technically no. In reality, yes. Bows require arrows and most spells require a material component. These are never tracked unless it's something special. If a spell costs thousands of gold in material components to cast, it should be required that you actually aquire that component, but otherwise pretty much everyone just assumes that you are prepared with a enough basic materials. The same for arrows and any other basic resources usually. I've never played with a party that tracks food and water, for example. It's just assumed you've come prepared.
I hardly have players even using arrows in our 3.5 games, but I do definitely require the expensive material components (like I know there's a spell that requires a ruby with 100gp or more). Most of them can be acquired easily enough that it doesn't matter (such as sulphur + bat guano) but if it's expensive/rare enough, I'm going to make sure you can actually get them.
I started a Pathfinder CRPG a few days ago and one of the classes is specifically designed just to do that. I was tempted to choose it but it had like the highest class difficulty and it's my first time playing so I played it safe and just went with a regular ol' sorcerer.
It's almost impossible to do that in a high stress environment without dropping the weapon, and if the shield is a buckler or a viking shield it's completely impossible due to how you hold the shield. In any case you make the shield unfit for blocking while holding the sword.
If you want to throw spells you should do as the romans with a small sword with a scabbard on the sword arm side and sheathe the sword to free the hand
While i dont have one of those shields irl I can easily hold 3 swords in one hand so I disagree. Besides if your opponent is just letting you do hand movements eitherway being able to block is irrelevant. Not to mention you can also hold the sword in the palm of the hand by facing the palm uppwards.