Around here, if you're going to put any type of motor on it, yes you do. And yes, that does apply to battery operated trolling motors.
If it's always going to be "oar-driven", then you don't.
Here in NY, those same rules apply. Quite a few states have that rule, but some do not require it if the boat is less than a particular stated length as a cutoff.
You definately need to give more information. As mentioned above, every state in the US has different laws. The same applies across the pond. The biggest annoyance in getting registered here in Virginia is the damn line at the DMV :facepalm:
You say that it "WAS" a tender. If it's no longer a tender and you put a motor on it, then yes, it must be registered. If it is a tender with a 9.9hp or less motor on it then it's up to the state you live in, as mentioned. Federal regulations (Coast Guard) do not require a "tender" with less than 10hp to be registered.