Can I get the Custom Fit perk bonus while wearing a Dragon Priest mask?

Is there any combination of heavy armor and a Dragon Priest mask that allows the Custom Fit perk to be active?

No, because as stated in @Nelson's answer, Custom Fit is a Light Armor perk.

However, there is an equivalent perk in the Heavy Armor tree called Matching Set:

Additional 25% Armor bonus if wearing a matched set of Heavy Armor.

This perk you can get while using a Dragon Priest Mask. All of the Dragon Priest Masks in the game (including the Wooden one) are classed as Daedric Armor - so wearing Daedric chest, hands and feet pieces along with any Dragon Priest Mask will fulfill the criteria to activate the perk.

No armor involving any Heavy Armor will activate Custom Fit.

The reason is Custom Fit triggers only on all Light Armor. Heavy Armor is obviously not Light Armor.

Custom Fit

25% Armor bonus if wearing all Light Armor: head, chest, hands, feet.