Yes, you can use them against your own code. Perhaps the easiest way is via arcpy, embedded within the documentation for IDW you can see a stand-alone implementation of that particular function. Based on your previous question though, it sounds like you have a specific problem: you want to interpolate the values for a few unknown locations within an existing raster layer. If that is the case, then IDW and the like are not the right approach: they're intended for use against layers where you have a limited number of data points and want to interpolate the surface entirely.
For just filling a few holes, a simpler method would be to just perform a focal operation on the raster and replace any NoData cells with the average value of its surroundings. There's another question which goes through the logic of using this method.