In other words - Does Brahman and humans who have achieved enlightenment have these Gunas?
I am answering from the perspective of Advaita Vedanta.
In Advaita Vedanta, AgyAna or ignorance is considered as endowed with the 3 Gunas - TrigunAtmikA. Other terminologies used for AgyAna are AvidyA and MAyA.
See the following flow charts, which I took from the concluding section of the book VedAnta SArah - Essence of VedAnta (Sri Sadananda Yogindra Sarswati; with commentary by Swami Amritananda):
The first flow chart is useful for our purpose. The characters are in Bengali and hence I am translating into English.
Definition of AgyAna (AvidyA/MAyA):
Four facets of AgyAna:
That means one can not explain what it is. It is neither Sat (true) nor Asat (false) and it is not even a mixture of both.
It is the embodiment of the 3 Gunas viz: Sattva, Rajah and Tamah.
- GyAna Virodhi
It opposes GyAna or knowledge and it is destroyed by knowledge too.
That means it can be felt as true or can be experienced and hence not unreal.
The 2nd chart gives the power of AgyAna viz: Avarana and Vikshepa but discussing those are irrelevant here.
So, in short, the 3 Gunas are part of AvidyA, which when destroyed, by knowledge, liberation is achieved. Therefore the Gunas exist as long as ignorance exists but not after that.
So, neither Brahman nor realized persons are affected by the Gunas.