The book says:
Concentration Some spells require you to maintain concentration in order to keep their magic active. If you lose concentration, such a spell ends.
So what happens if, for example, you are already concentrating on a spell, and cast Witch Bolt without concentrating. Would you get the initial arc of blue energy, or would it not even go off?
I am asking if you can cast a spell that says concentration without concentrating for an immediate effect. This would be useful to avoid interrupting your existing concentration. In essence, if you are concentrating an thing A (doesn't have to be a spell since other things need concentration), can you cast a concentration spell getting an immediate effect without losing concentration on thing A?
Since the definition of concentration is to keep the spell active (meaning it is already active) I would think that you would get the initial effect (if it had one) with out the need to concentrate on it.