While it is true that if you're shooting only under red light your camera will collect less light than if you had full spectrum lighting you must also keep in mind that all of the light you are collecting is mostly going into only a quarter of your sensor's pixel wells. The lack of green or blue light in the scene doesn't increase the amount of red you can capture before the red is totally saturated and you begin to lose details in the highlights. You still must expose so that none of the color channels are allowed to blow out.

Another question here perfectly illustrates what happens if you try to increase exposure when shooting under very limited spectrum lighting: Blown out blue/red light making photos look out of focus

When shooting under only a single color of light it is probably more crucial than ever to check the RGB histogram to be sure you're not completely blowing out one of the color channels. Due to the lack of green or blue light, looking at a combined histogram will make it seem like you're underexposing even when red is completely blown out! If your camera, like most, has a monochromatic light meter it too will probably recommend exposure levels that will blow out the only channel of light you are actually capturing. Cameras with RGB+IR light meters are becoming more prevalent and tend to do a much better job of metering in such light, but setting exposure manually is, it seems to me, still the best option.

Also keep in mind that the Bayer color filters are not absolute. The green filtered pixels do not reject 100% of red and blue light, they just let a higher percentage of the green light through than the red and blue light that strikes the filter over a "green" pixel well. Some red and blue light makes it through the green filter. A good bit of red light (over 10% in the example below) will be registered by the green filtered pixels. The blue filters let a significant bit of green light through. Even a small amount of the red light that lands on a blue filtered pixel will be included in the photon count for the "blue" pixels. Each pixel well only registers a single luminance value and can't tell the difference between red, green, or blue light that makes it through each filter.

The reason LED lights don't give us accurate color isn't necessarily because they are dimmer than more full spectrum lights, it is because they emit a narrower spectrum at whatever brightness they emit. When we combine a red, green and blue set of LED lights, they still don't emit light at a lot of wavelengths that some objects in the photo would reflect if light at those missing wavelengths were present.