Thank you for your question!
Yes, it is certainly possible. As a matter of fact, there are some non-BK souls who have that experience and they do not need to settle their karmic accounts to have it.
There are different “degrees” of soul consciousness, because as we are aware; we are “numberwise.” A “newer” soul maybe able to experience soul consciousness but the degree is not the same as a Brahmin soul; for their experience of duality are not the same. A Brahmin soul has greater experience of duality.
Through yoga, a Brahmin soul will emerge sanskaras which are from the Golden/Silver ages, because that is what his role entails. Therefore, that experience of soul consciousness will emerge such sanskaras. This is what BapDada calls “following the Godly method” or to experience “Divine virtues.” On the other hand a soul who has not experienced the Golden or Silver ages, does not have those sanskaras from the Golden and Silver ages; even in his experience of soul consciousness.