Fantastic question Bob. One I’ve never thought to contemplate.
My gut answer is yes. God, by definition, is omniscient and omnipotent, and one of the primary reasons we, as social animals, choose to be surrounded by people is because they provide us stimulation. Both on a physiological level (laughter, nervousness, adrenaline, arousal etc) and an intellectual level (discussions, analyses, complex social interactions etc). Given that a God would already be aware of what any being is thinking, feeling and planning at all times and would also be capable of altering himself physically all of these notions that encourage social interaction would lose their appeal. And when one has no motivation to interact with other beings that can easily lead to isolation and loneliness. In short, it’s possible that God is lonely for the same reason Dr. House is lonely, others don’t provide him the stimulation he craves so he attempts to find it via alternative means. Following on from this it’s even plausible that, assuming the God in question created the creatures of Earth, we were constructed as a means of keeping God occupied to divert from the aforementioned loneliness.
On the other hand, one could say that for the very same reason God isn’t lonely; if God is capable of sharing in an organisms every titillation it may accordingly feel a sense of connection with said organism. But this is presuming that a God has the desire to feel empathy as from their all-knowing perspective it may simply be seen as a dysfunctional and destabilising notion.
I’d speculate on the matter further but the possibilities are seemingly infinite. It’s a remarkably thought provoking question for which I’m grateful.