Would a video processor help reduce input lag for gaming?

The video processor lag will be ADDED to the lag your display has when being fed it's native resolution. You can usually use a video processor to reduce the lag your display introduces when handling 15khz sources (240p, 480i), but you're out of luck if you only feed progressive signals like 720p or 1080p.

because most TV sets need considerably more time when processing a 15khz signal like 480i. 15khz signals need to be deinterlaced and if the TV set has a motion adaptive deinterlacer then at least 2~3 frames have to be buffered for analysis. Progressive signals on the hand hand, just have to be scaled and what reviews usually test are HD signals from a 360 or a PS3.

If you now take a video processor with a fast game mode for processing 480i sources, then you get the "fast scaling-only" delay from your TV plus the time the processor needs for deinterlacing (which is usually faster than having it done by the TV itself).

because TV don't have a "bypass" function. The signals run through the same processing (deinterlacing, scaling, postprocessing) no matter what resolution they are. Usually at least the deinterlacer can tell if it's needed or not, so the delay for progressive signals is lower than for interlaced ones, but the rest of the processing time stays the same.

TVs overscan even when fed native res unless you use 1:1: whether it still goes through the scaler chip I dunno.

If you run progressive HD content through a video processor, the lag will increase. *Most* (not all, but really most) TVs show the same processing delay for 720p and 1080p feeds (again, caused by the same processing path for both signals). If you add an external scaler, it's delay will be added to the TV's delay.

This said, most external scalers are quite fast when processing 720p signals. DVDOs for example add 6-7ms.

The XBox360's internal scaler in mandatory, so you have no way to compare it to an unscaled output. The XBox games run at all kinds of internal resolutions. Most run at something between 540p and 600p with widely ranging horizontal resolutions. Games running at the sweetspot (1280x720 or 1920x1080) are rare. It's a myth that most 360 games are 720p native. When review sites or magazines refer to games running internally at 720p, you usually just mean that their native rendered resolution is CLOSER to 720p than to 1080p.

For example Halo 3 runs internally at 1152×640.

There are visible differences in scaling by different displays or processors. 720p to 1080p is much easier though compared to 480p to 1080p. For XBox360 and PS3 it's a no brainer for me. Directly into the TV is the easiest way, has the lowest lag due to no additional processing and is the cheapest anyway.

480p (Wii, Cube, PS2) is a whole differenent matter though. Here external processors can give you a considerably better picture which might be worth the extra lag introduced by the scaler.

for HDMI output the DVDO processors in gamemode are pretty fast (0.5 frame delay). For VGA output the XRGB processors (2, 2plus, 3) are even faster.