No, I don't suppose that there is any particular connection between the two other than as fellow Catholics. But I've stumbled across a few references while reading St. Bede that were amusingly interesting to me (and maybe no one else).
The office of "thain" is apparently ancient in England. St. Bede refers to one in II.9, named Lilla, who saved the king's life by taking a poisoned sword for him. According to notes in this edition of EH, a "thegn" (apparently the old Anglo-Saxon spelling) would have been not necessarily a bodyguard (as this little anecdote might suggest to a modern reader) but a member of the royal household; reference.com describes the thegn or thain as a "minor noble."
The poisoned sword that Lilla took for king Edwin was thrust by the assassin Eomer. Ha! (laughing not at or even near the honorable Lilla, but rather at Tolkien's source of a name).
Lastly, in II.5 Bede refers to a Kentish dynasty surnamed Oisc as oiscingas. So we see in these references that if I had known for all these years a little more English history, I might have known better how much Tolkien drew upon it in crafting The Lord of the Rings. Although I find it hard to imagine any sense in which Eomer son of Eomund has anything in common with an assassin except possibly in the twisted mind of Saruman :-) But I do find it interesting that the "ingas" suffix used in reference to a dynasty isn't something that Tolkien invented at all (as I thought) but is something he took from his own heritage.