Firstly - wow was not aware this was coming out, took me a few minutes to recover from that!
Tom Bombadil I think is important in that he gives a little insight into Tolkein's mentality (which you can't really recreate without living through the world wars or something similar as he did and therefore has some value), kinda annoying he wasn't in the film, or the old forrest or barrow wights for that matter..
Tom Bombadil I think can only do what it is in his nature to do and he is completely neutral so of course why would he? Sort of representative of the way nature carries on regardless of the wars and politics that trample over it and that it would survive this war (war of the ring, WWII for Tolkein) regardless the outcome (as Gandalf said there would be no point in giving Tom Bombadil the ring, because he would not think it important and probably lose it). That said as all things eventually wither and die except TB I suppose if you were going to pile metaphors on top of each other he would eventually overcome Sauron regardless.
It would seem that Amazon are saying the series will precede the Lord of the Rings storyline and will be based on Tolkein's writings, Tom Bombadil has existed since the creation of the world so it is feasable that he could appear but I don't really see in what context and I don't see that they can really build any on his character. Would think that the series would be primarily focused on teh Silmarilion, possibly the Unfinished Tales and perhaps also The Children of Hurin and there is more than enough material there to work with. I thought that Beren and Luthien could be a film in it's own right for a start. More likely though that they will want the story to relate directly to Lotr so I suppose the background of the creation of the rings, and maybe the storyline of Sauron from maiar smith to satanic being.
Would be really nice to see Valinor and Numenor depicted in film though not sure whether that would be done well.