even talking about CW or not, 2 different, single line lasers (although real CW doesnt exist, every laser has a finite bandwidth) can be coherent with each other or not.
In the case of the 3 different sources where you then combine them together, well, yeah those are incoherent with each other, but for example when you have your 532nm laser, the fundamental (1064nm) and the green are coherent with each other...although they have different wavelegnths
*EDIT*
Forgot about you Chipdouglas:
Well, what i meant to refer was that when you have a "white light" (i put it in "" because by that im just meaning a very broadband light source, be it in IR or VIS) laser, that is completely coherent, that (modelocking) is possible to do. While when you have a normal light source you cant (well, I guess that it might be possible to make everything coherent using slits and what not, but in the end your output will be negligible).
I meant that in order to have all the electric fields constructively and destructively interfering with each other (and hence producing those pulses), all the light components need to be coherent with each other. In other words, if they wouldnt be coherent, perhaps you would be able to create a pulse, but localized in time and space, as you dont have coherence to keep it going forever and everywhere.
To give an example of how awesome light is:
When you have a single line laser, you can perform the famous double slit experiment and see the interference pattern on the wall. That is a spatial interference. When you have a coherent broadband source, and you make them interfere, usually you look to the frequency domain instead and you are able to see a modulation of the spectrum, just like the fringes in the slit experiment, but in this case you see them in a spectrometer.