You can use the image modes in PS in many different ways with the gradients. The key thing is whether you add them before or after the conversion to the different mode. You set the mode via the image menu and mode and then you will see a selection of CMYK etc though which ones are active depends on which one you are currently in. In the same menu you will also see a selection of 8bits / channel 16bits and 32bits. If you are in RGB then you will see the options to convert to Grayscale as well as LAB as well as CMYK. If you are in CMYK then you will see the option to convert to RGB or LAB etc. If you wish to create the color effects in duotone or tritone then you will have to first set the image into grayscale. I would suggest if you have created the color effects before hand that you use the adjustment filter and black and white to convert the item into a grayscale before changing the mode to grayscale. Once you are in grayscale then you will see the option to convert to duotone etc (you will notice when you convert that it offers the hint to use image adjustments). The key thing with the duotone is that you have to enter a name for the inks etc (which I must admit I find slightly annoying as I wish it would just add the names duotone channel 1 and 2 or something). Once you have converted the mode then you will find that many of the effects and the blending modes are not available. The gradient tool, however, is available and you can add multiple applications of the tool either to the background layer or perhaps other layers (which does mean you can modify the blending modes and opacity as well as remove or recolor the layer at a later point). You can edit the preset in RGB / CMYK etc and will see a slightly different color picker (stop color) when you select a stop and go to the color picker.
If you use the 32bit 16bit then converting back generally brings up a dialog for the HDR contrast and you can then modify the settings to achieve either a surreal result or something very similar (visually anyway) to 8bits. With the conversion of CMYK etc to RGB the result will change and you may have to use the adjustment controls or layers to tweak the colors to return them to much the same as in the color mode (visually anyway) though, of course, that is not always possible if you are converting from wildly different color modes and profiles (not going into the profiles side of things as that is a vastly complex area and probably not of much interest if you are just using the different modes to create unusual color imagery for the web etc)
Below, the grayscale form of the previous RGB
From the grayscale to a blue duotone
You can go from 8bits to 32bits per channel very quickly, going back to 8bit (and to use the save to the web) you have to use the HDR toning dialog and you can use that to get a very similar result or you can use the dialog to create some truly extreme color effects as well as creating some very unique color imagery