Eh, but the lightgun for the Atgames Legends Ultimate is just a Wiimote; same sensorbar, same basic camera-in-the-controller technology. I would imagine it'll have the same lag and the same need of an on-screen reticule as the Wiimote, since you're orienting all your motion to the sensorbar rather than getting signal from the TV itself. (It does have the advantage of knowing EXACTLY how big the TV is since it's a standard size, and it will probably work fine for the majority of arcade lightgun games since they're based on strafing the enemies with cabinet-mounted machinegun fire in say Revolution X rather than something like Point Blank where you're bullseyeing each shot.)
I wouldn't count on it to be the right gun technology for a Time Crisis. You can see somebody here with what looks like an arcade TC1 using a Wiimote hack, and he really needed the on-screen cursor (which is part of the emulator I guess? PSX and Arcade Time Crisis didn't have that big aimsight, as far as I recall?) to keep up with the play.