It's not the delay, it's the fundamental technology. The duck hunt gun works by using signal processing on the timing of the scan-line. On an LCD TV there is no scan-line so it just doesn't work at all.
No, the Duck Hunt gun doesn't time the beam to the scanline. It and the software only care about light level deltas from one frame to the next, looking for the dark-light-dark sequence. It fails on non-CRT TVs not because there's no line scanning, but because they buffer and delay the display enough that it falls out of frame synchronization with the software.
Other light guns (including the SNES Super Scope) and light pens do sense the pointing location by timing when the TV electron beam crosses the gun's sensor, but not this one.
