There could be a line on a circuit board inside, that changes state when a valid signal is coming in. If you could tie this line hi or lo (whichever is needed), then you might force the screen to always display whatever's incoming.
However it might not work either. Digital transmission is not like analog transmission. We have analog vcr's that show a blue screen when no signal is on a tape being played. If I fast play forward or rewind, that's when I see the snow on the tape.
However with digital, if the signal is unsuitable, the digital screen may not even display snow. Snow is not supposed to be part of the digital vocabulary. It may show the last image received, with block mismatches, or pixelation, or other odd effects.
From my slight experience with digital equipment when it loses signal, there will be a moment's pause while it checks to see if an acquired signal is strong enough and consistent enough to be displayed.
In other words, it may not work if you rig a signal generator at the same reception frequency, either inside the screen or as a wireless. Your screen will probably perform the same length of delay as it switches between your data source and your alternate source.