F-1 working with CPT while green card pending

I'm currently on F-1, but I'm waiting for my marriage-based green card interview date and work permit (I already did my biometrics). I wish to apply for CPT for an employment opportunity directly related to my course of study (I'm a Ph.D. student and already used my OPT after my master's). Will this in any way conflict with my ongoing marriage-based green card application? Thank you