Does a shield +X give the +X bonus without wielding it?

[Witty Username]

I would say picking up a shield would be part of the action donning it.
I might say you need an action to pick up a shield, if it is something like a viking round shield I could see that being a bit complex to grab and carry efficiently in quick fashion. But that that would also Don it.

I would like to say my ruling has been validated by RAW.
Specific overrides general. therefore object interactions and holding doesn't apply to shields as the donning rules overrides them. So you cannot simply hold a shield.
Don: "this is the time to put on the item"
Shields: "A shield is carried in one hand"
Therefore: you must don a shield to carrying in one hand.

Now I will fully admit this is making trouble, but it is RAW.