As you are probably aware Wikitree relationship finder does not return a potential trail between Walter Norton and any of the Surety Barons. I think this is because the upper branches of this family and collateral lines are not documented and stop with his most distant paternal ancestor, Unknown "7th LeSigneur de Noruile" Norton (1284-1330). As much as I would like to be able to say whether there is or is not a Magna Carta connection without having to do research into the family tree of Walter Norton I can't. Perhaps there is another Wikitree member with more knowledge of this Norton line and collateral branches who could provide more information ?
I would check out the NEHGS article however I do not have a paid membership which is required. There is information to be found on Walter in the following references but they do not seem to shed light on your question:
*"The Great Migration Begins" (Robert Charles Anderson), pp. 1339-1341
*Genealogical Dictionary of Maine and New Hampshire (Noyes-Libby-Davis), pg. 514
Norton is not listed in Douglas Richardson's book, Magna Carta Ancestry pub. 2011. as a known MC Gateway Ancestor. Additionally, a quick online search and review of his Wikitree line indicates that the ancestry of Walter Norton is currently questionable and unproved. Further research may prove to be helpful in determining whether Walter has Magna Carta connections however there does not appear to be anything in the readily available sources that indicates a Magna Carta connection based on the information we currently have on his line.