Visible light is measured in lux, such as 0.05 lux or 0.1 lux. However, infrared light cannot be measured in lux, because it is invisible.
The most common way to measure infrared light is in watts/ M² or Ft², or the energy produced by an infrared light source over a specific area. Most camera manufacturers do not test or specify sensitivity to infrared light. Oftentimes light sensitivity to VISIBLE LIGHT specified in fractions of lux, such as 0.1 or 0.001, but it is not applicable to infrared light.
Hence it is impossible to tell how well will the infrared illuminator will work with a particular camera without testing.
So, what exactly is your question? - As you mentioned yourself, you can use W/m² or something in that manner to quantify radiation of any given wavelength. Furthermore, each camera has a known spectral sensitivity that is wavelength dependent, as you also pointed out yourself. If your camera is not specified for infrared light, it might be just not suited to detect it.
If it is suitable for IR detection, your CCD chip will have a spectral sensitivity or spectral response curve.
However, I am not sure what you mean with "will work well" - what does "well" refer to? - high sensitivity? Good spectral resolution? Short exposure time?...
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