Will having depression or anxiety also cause me to have delayed sleep phase?

Maybe: Circadian rhythms can be affected by the timing and amount of light your eyes receive. Our rhythms can change if we engage in behaviors that disrupt our timing of light. For instance, if we consistently sleep in later or stay up late, we may not get sun light appropriately to re-synchronize us. People with depression often have insomnia which can potentially affect circadian rhythms.

Not automatically: Many depressed and anxious people do have initial insomnia, or difficulty getting to sleep. But delayed sleep phase syndrome (dsps) is different and much more persistent -- can exist without depression or anxiety. Your physician can prescribe medicines to help insomnia that comes from depression/anxiety, and it should remit. Dsps can also be worked with -- but the approach is different.