I agree with OP Tipping - I think it would be very hard to tell if for certain if the phrase is being used “ironically” (in the sense that the speaker is mocking the vey idiomatic phrase that he or she just used). The phrase, I think, has always been whimsical and somewhat “jokey”. So discerning whether a writer or speaker is “joking” about the whimsicalness of the phrase or about the fact that it is a somewhat “old fashioned” expression would be a tricky task without a very, very deep exploration of the context in which it is used in a given example. But, FWIW, in the instances where I recall hearing it, it did not seem to be used for a sort of kitsch effect: the expression was used playfully, but the speaker was not necessarily making fun of the expression itself for being dated.
And I’m not sure that it is dated in the same sense that an expression like “groovy” or “grody to the max” is: the latter had a shelf-life of being fashionable of about five seconds. Soup to nuts has been around for a while, and I’m not sure it inherently produces eye-rolls the way “grody to the max” does. (groovy seems to have made something of a comeback, as I have heard it used non-ironically in some TV and radio shows, relatively recently).
Finally, I would note, FWIW, that I seem to hear “soup to nuts” used more by east-coasters of the US than west-coasters. I’m not sure if it’s a regional thing or if it is just a coincidence that I’ve pretty much only heard it used by such speakers. The expression has always seemed a bit odd to me and took me a while to decode, because I’ve never had a plate of nuts as the last course of a meal, so the underlying metaphor was a bit obscure (I also wondered, and still wonder to some extent, if “nuts” is being used as a bit of a double entendre, but, if it is, does soup also have a correspondingly naughty sense? If so, what on earth would that be?). But, nonetheless, I’m not sure it’s really that “dated” (something can, after all, be old without being dated).