Yes, it should be that simple.....keep in mind that when you are driving the voltage is more like 14VDC.
Can you post a picture of the power pack's label?
So...to be clear.....presently the power pack is supplying the juice for your LED strips and you want to determine if you can ditch the power pack and connect to your house batteries?..
What diode are you referring to? The lump in the cable is a ferrite (magnet) to pass EMC emission requirements for UL, CE marking.....you don't need it, things will be fine without it.
BTW pretty much all 12VDC barrel connectors have the positive in the inside and the -ve (common) on the outside of the barrel....so you don't smoke the power supply by having the connector touch a metal table top, etc.
Those std barrel connectors typically have 2 or 3 internal hole sizes 2.1mm, 2.5mm etc. If you have a caliper, very easy to measure.
Digi-key, mouser (and highly likely ebay) sell the connectors. I have a small pile of them, so if you know what hole size you need PM me....I can send you one.
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