Dale, the double and triple negatives make it difficult for me to follow exactly what you're saying. Plainly disproved that ... could not have had?
I think you might have muddled several different lines of discussion.
First, Edmund Rice is I1. That much is clear, but he's too distant from John Rice, also I1, for them to have been close relatives.
Second, the Edmund Rice pedigree as published in By The Name Of Rice is bogus. It goes through a man who never existed, then back through a man who has been fraudulently connected to a more famous family on the other side of the country -- even though the sources actually show the connection was impossible. The dates are a jumble, the places are a mess. It's just pure fantasy, a typically American delusion for that period. So, there is no particular reason to think that either Edmund Rice or John Rice came from this Welsh family.
Third, study after study shows that I1 is primarily, if not exclusively, associated with the Anglo-Saxon and Norman invasions, which is why it's concentrated in the areas they settled most heavily. I quibble with this, just a bit, but a new study published just this week showed very strongly that the Normans and the Danes made very little impact on England's DNA. My quibble, such as it is, is that I don't see much evidence that Anglo-Saxon, Danish, and Norman DNA is all that different. The epicenter for all of it was Denmark or just south of Denmark.
Fourth, Rhys ap Thomas came from a very old Welsh family, with a pedigree going back to the earliest tribal leaders, before the coming of the Anglo-Saxons, Danes, and Normans. The overwhelming odds are that they would be R1b, but perhaps some chance that they have Roman ancestry, so maybe one of the exotic groups like G.
Fifth, no one knows the haplogroup of the Tudors and there are too many outrageous claims to noble Welsh ancestry, so no one is really sure, but the odds on favorite with the existing data is that the Tudors will turn out to be R1b like the many modern men who claim to be their distant cousins.
Sixth, a woman who marries into "both" lines has nothing to do with their yDNA. Her sons will always have the yDNA of their fathers no matter who their step-fathers might have been. I think this is often a sticking point for you because you don't quite keep the elements separate. My dad was G2a and so I am. My first step-father / adopted father was R1a. My second step-father was E1b. I'm not likely to go off the rails and start looking for R1a and E1b people to find ancestors on my G2a line.
So, my answer to your question would be (a) I think Rhys ap Thomas was almost certainly R1b. I'd be surprised if he wasn't, but I wouldn't bet the ranch on it. And (b) Rhys ap Thomas could have been I1 if only because there's no proof he wasn't. There's always a chance that some stray I1 Dane washed up on the Welsh shore, was there to welcome Joseph of Arimathea, and founded one of the main noble families. But I wouldn't risk even $1 on it.