The Status"box" its amplifier is a 12 Volt DC device, not mains so to work must have a 12 VDC feed.
How is yours wired up to be supplied with its required 12V DC?
Typically, the "box" has a permanent feed, only switched by the "box's" own switch.
Has it been in your case wired from the same plug used to power the TV so requires that to inserted?
Again, typically, many dual mains and 12V DC TVs used in caravans and MHs will be factory or dealer wired to always be powered by the 12V DC option. Done that way it does not matter if on an EHU or not, as the TV and aerial work in just the same user way.
There is no concern of depleting the battery's 12V DC when on an EHU as that is being charged by the EHU also, therefore it is pointless wiring a dual voltage TV up to a mains socket.