That's a very general hypothetical, but short answer, yes it is "possible," but much less likely to be "provable." It just depends on the particular family and ancestry of the particular individual, as there are lots of ways that a commoner could have royal roots. I have tons of royal roots in my English ancestry, but this was because most of my ancestry that is English came to America back in the 1600's and had land grants from the king, so were already prominent, and many of those were descendants of younger male siblings or females, i.e., non-inheriting nobility which then going up through the generations eventually I had lines that went to King Edward III or earlier. However, I also am part Swedish, and I have done pretty extensive research on my Swedish lines for what is available, and in the research I did, it showed they were all farmers of a peasant or yeoman class, and that they didn't ever mix with the nobility and royals, at least none of mine did. They were always farmers, maybe not always poor, but were definitely not moving around much, either geographically or through social classes. However, I did have some lines that were church people, i.e., reverends and some who were soldiers, who did well and were raised to a bit higher standing in their respective posts either in the Swedish churches or military regiments, but I could only get back to late 1500s early 1600's for those two branches, and perhaps those lines might go back to nobility, but probably not, I don't know, because I can't go back farther, but as for what I know, there's no whiff of any royal roots with those lines. There definitely was whiffs of noble roots though in my English lines, because they founded towns and stuff, so were already pretty big stuff, even though they themselves weren't nobility, when they arrived in America. But to have that kind of ability to come to America and not be somebody else's indentured servant, and to be given a land grant by the king, it was obvious they were important enough to be able to have the "potential" of having noble roots. And sure enough, most of those lines, do go back to royalty but it's a ways back, as Edward the III, who is my most recent royal ancestor, was born in 1312. Some didn't though, as I am a direct descendant of the first governor of Massachusetts, John Endicott, and as far as I know, he comes from pretty humble roots in Devonshire. So it really just depends on the individual family lines.
So yea, if you can find the family tree of an individual of all those things who is a commoner and who might have royal ancestry, but you gotta find it. I certainly would never say its not possible, but depending on how "common" they were, and in what point of time you can go back, and are still found to be common, greatly helps determine the liklihood of whether they could have royal connections or not. For example, if you can get back to early 1700's and the family tree shows their ancestors were still peasant farmers, then very unlikely you're going to find any nobility, let alone royalty. It also depends on how far back you're willing to go for purposes of having royal ancestry. I mean, they say all Europeans could be descended from Charlemagne, who was born 742 AD, so if you can get back that far, then you might find some connections to Norwegian royalty, but that's Viking times, and the Vikings unfortunately don't have much as far as written records go, so you'd probably never know. But is it possible? Of course it's "possible", as well as having ancestry from other European royalty, probably even Charlemagne, but for most people, they would probably never be able to prove it if they did.