Yes, you can. Such components are called hybrid components . They work in a wide wavelength band, because the DOE dispersion is designed to compensate the material dispersion. I acquired a 3x3 beam splitter. When I tested the component with my laser pointer, I observed a bright spot in the center of the diffraction pattern.
Diffractive components are strongly wavelength dependent.
Probably your component is designed for the wavelength of HeNe laser, 632.8 nm. On the other hand, your laser pointer contains a semiconductor laser with the wavelength 670 nm.