NFC battery draining through constant use Does putting a device that constantly checks/uses NFC affect/drain the battery? One example is Dimple IO which puts NFC buttons on the back of your phone.
The Tag Dispatch System of Android Developers  says


  Android-powered devices are usually looking for NFC tags when the screen is unlocked, unless NFC is disabled in the device's Settings menu. When an Android-powered device discovers an NFC tag, the desired behavior is to have the most appropriate activity handle the intent without asking the user what application to use.


Therefore, your device is scanning for NFC tags, when the screen is on , so power would be used.
My guess , is that this power consumption would be low, and not cause a drain on battery, since


NFC is low power meant to exchange information within 5 cms
NFC is active only when screen is on
Since the tag information may remain unchanged, it may not require frequent polling
NFC isn't quoted as a battery hogger in the battery drain culprits list (subjective)


Specific to your question, it would depend on


How well the app optimises power ( it is not compatible with my device to see behaviour)
NFC chip level power consumption used in your device 
How doze optimises (if using Marshmallow)


I would think that power consumption would be negligible, but it is a good idea to verify using an app like  GSam Battery Monitor to see the actual power consumption and you could post your findings as an answer

Edit: Answer to Does NFC drain power if tag is attached constantly? on Electronics SE gives good technical reasons for why the consumption should be low