The G-quadruplex appear normally at the end of DNA sequence (telomere region) but apart from this many promoters in which some of them also acts proto-oncogenes have the G-rich region which responsible for forming G-quadruplex. So in this sense yes they are form naturally. Not only G-quadruplex the cytosine bases also form such unusual structures called i-motifs. So it might be possible that during stress or infection there could be the increase or decrease in the formation of these unusual structures as most region encodes vital gene sequence crucial for cell survival. Apart from this the m-RNA after transcription may form such structures too.