Is it possible to speed test a film with a B&W densitometer for C41 and E6 films?
I'd say essentially not possible, at least not with any useful accuracy.
To give you some idea why, take a look, for example, of a Kodak Portra film data sheet. There will be a graph called Spectral-dye-density curves or something to that effect. It shows the spectral density of both the D-min (clear film) and a midscale exposure. You can probably get an idea of how "vague" the meaning of a b&w densitometer reading will be. If this is not apparent just try to decide what is the density difference between the two plots. (Fwiw a b&w densitometer typically uses a "visual" response, roughly the overall sensitivity of the human eye in bright light.)
By way of comparison, a color densitometer sees three narrow spectral zones, representing each of the three color dyes. With such a densitometer you can actually graph three separate curves from a neutral exposure. So there will actually be three speed points: one for each color layer. Ideally you have exposed with the proper light source so that the three speed points are nearly the same. If the exposing light is different from the film's aim "color" then at least one of the color-layer "speeds" will be offset from the others. As I recall the ANSI method "weighted" the individual color speeds to get the final film speed. Anyway, it is not as straightforward as a b&w film is.
Is there a particular issue you are trying to look at? If so you might get more useful results from a film scanner (I understand that you have such for your business?). I'm guessing that it's possible to put the scanner into a locked-down manual mode and to somehow correlate the results to density values. Or perhaps you might be able to get some useful data by sandwiching specific color filters with the film to roughly isolate a color layer.