I do not think that this is a good theory, to be honest. I hope I can say that without offending you. I am also not sure why it would matter all that much what “day” we are supposedly in right now. What would be the practical or theological implications of such a thing? This sounds like mostly speculation, which is not all that useful, in my opinion.
But, since I am pouring cold water on this, I better explain myself. I suppose one could reasonably propose that we are now living in an sort of extended 7th day, given that Genesis talks about the 6th “day” being completed, and God resting on the 7th “day.” So, if one wants to make an argument about which of the creation days we are in, then one can possibly defend that we are in the 7th day, but not the 6th.
But let me add, that this is highly speculative. There is no Bible passage which proves that the 7th day of creation extends through current times. This 7th day, which is a day of “rest” for God is at least on some level metaphorical, is it not? Did God “rest” for exactly 24 hours? The Jews and the Christians use this idea of a day of rest in a somewhat metaphorical sense (for example in Hebrews 4:4-7). So, what would it even mean if we were living in the seventh day?
So, here is my answer. First of all, no, we are not in the 6th “day.” This makes no sense at all as far as I can see. We might possibly be able to propose that we are in the 7th “day,” but this would be pretty much purely theological speculation and not particularly productive speculation at that, since the Bible does not specify such a thing.