From a Theravada point of view, a Buddha is an enlightened human with perfected insight and wisdom who lives in a human realm until he passes away into parinibbāna; at which point he would cease to exist. As an enlightened human with perfected insight and wisdom, it would not be possible to experience obstruction to awareness.
From some Mahayana points of view, we are all Buddhas already:
Another way of putting this is to say that Buddha Nature is "something" -- perhaps not the right word, but I don't think there is a right word -- that you are, together with all beings. And this "something" is already enlightened. Because beings cling to a false idea of a finite self, set apart from everything else, they do not experience themselves as Buddhas. But when beings clarify the nature of their existence they experience the Buddha Nature that was always there.
(The above is a very basic reference to Buddha Nature, but I didn't want to get off topic with too much detail of something I am not well versed in.)
The concept of Buddha Nature also allows for non humans to be Buddhas:
The Lotus Sutra, written between 100 BCE and 200 CE, further developed and popularized the doctrine of the Buddha-nature. It influenced subsequent later sutras.
The tenth chapter emphasizes, in accordance with the Bodhisattva-ideal of the Mahayana teachings, that everyone can be liberated. All living beings can become a buddha, not only monks and nuns, but also laypeople, śrāvakas, bodhisattvas, and non-human creatures. It also details that all living beings can be a 'teacher of the Dharma'. Source: http://en.wikipedia.org/wiki/Buddha-nature
So from this point of view, with all beings as part of an enlightened "something" many of whom do not experience their enlightenment due to delusion of a separate self; it would be possible for a Buddha of any realm to not know they were a Buddha.