Should I mention an informal research intern in my CV?
You have scientific research experience relevant to the position you're applying for, so explain that experience in your application.
You can mention that you worked with graduate students and you could even ask one of them for a letter of recommendation. You cannot mention working with a professor, because you didn't, nonetheless, they may be willing to write a letter of recommendation that mentions that you worked with their graduate students and they could perhaps quote one of them for the details.