No, it's an adjective referring back to the subject, and as such must agree with the subject. Similar examples from the Treccani dictionary (from http://www.treccani.it/vocabolario/tutto/):
Riferito ad altre espressioni aventi funzioni di predicato: è un uomo [tutto] d’un pezzo; una ragazza tutta pepe, tutta fuoco (in tutti questi casi, l’agg. tutto concorda sempre con il soggetto)
There seems to be some confusion here. According to Lo Zingarelli Vocabulario, the idiom exists in two forms:
"essere/stare tutto naso/orecchi/occhi/gambe, ecc." meaning to have a nose/ears/etc. so large as to seem impossible to ignore, or to be all nose/all ears/all legs. Here "tutto" has nothing to do with the subject, nor does it change with the following noun.
"essere tutt'orecchi, (o tutt'occhi)" meaning to pay close attention; to listen or watch attentively. Because of the elision, the form of "tutto" is not clear, but it is clear that it has nothing to do with the form of the subject; it should probably agree with the following noun.
None of your examples from Trecanni seem to fit this idiom very well. Probably either subject should be accepted (I or they).
I don't have that dictionary here to check, but searching around, you will find many examples of variation in gender and number with this idiom, particularly the feminine "sono tutta orecchi," with the second meaning you cite. I'm not sure of the official rule, if it exists, but in practice it does seem to agree with the subject. There's even an example of the feminine form here on Duolingo: https://www.duolingo.com/comment/998140
I pulled those examples from the dictionary because they have the same structure (a noun used to describe another noun preceded by a form of "tutto") and the dictionary (at least that one) specified that in those cases "tutto" agreed with the subject. But if you have further information, sono tutta orecchi. : )
Grazie per la tua risposta. Compare these two:
Nella vignette il presidente Obama sembra tutto orecchi. (He seems to be all (or totally) ears.)
L'Obama ascolta bene, sempre è tutt(i)'orecchi. (He is always all ears.)
This seems to be similar to an earlier Duolingo sentence:
Siamo tutti bagnati (All of us are wet).
Or Siamo tutto (o completamente) bagnatti (We are totally wet).
Are these differences real? Or is my English ear making things more difficult than they really are in Italian?
Comunque, spero che tu sia tutt'orecchi, ma non tutta orecchi.:)
Hmm, your examples with "bagnati" are correct, but keep in mind that in those cases "tutto" is being used with an adjective rather than a noun. The examples I gave are with a noun, and it does specify that they should agree with the subject. However, now that I'm looking into it, I'm finding about the same frequency of use for "siamo tutto orecchi" and "siamo tutti/tutte orecchi" (the idiom isn't that common in the third person, which, combined with the overlap in verb forms, makes searching for examples with "they" difficult). So in practice it looks like it goes either way.
I don't think that the distinction between "tutto orecchi" and "tutt'orecchi" is consistently recognized in practice, if it does exist. Googling "tutto orecchi" I found this quote that plays off of the two meanings, but uses the same form for both (from https://books.google.com/books?id=lHZ3s16JV8UCpg=PT85lpg=PT85dq=%22sono+tutto+orecchi%22source=blots=fYVUXeTW_1sig=rHfwBCJ5GJ1IW6kwUv3pL7511s4hl=ensa=Xved=0CE0Q6AEwB2oVChMIrK7Xx_nYxgIVChw-Ch2_uAyN#v=onepageq=%22sono%20tutto%20orecchi%22f=false):
"Chieda pure" replicò Andrea con tono confidenziale. "Sono tutto orecchi!"
"Già, tutto orecchi...come lui!" ripetè fissando gli incredibili ciuffi di pelo che fuoriuscivano dalle enormi orecchie di Pierclaudio.
The majority of the results, at least on the first few pages, meant "I'm all ears" as in "I'm listening/paying attention." There were a couple that were clearly playing with the idea of being physically all ears (like in the quote above, or in a picture of an elephant), but as far as I can tell "sono tutto orecchi" and "sono tutt'orecchi" are interchangeable.
You have gone far out of your way to pursue this. I am grateful. If by some accident you come upon a definitive answer, I'd appreciate your passing it on. And I will of course reciprocate, if I should be so lucky. If life were always easy, it wouldn't be so much fun, would it? Grazie tanto.
In this particular idiomatic expression, "orecchi" is more common. In general, "orecchio/i" (masculine) and "orecchia/e" (feminine) are considered interchangeable, but for some reason the masculine "orecchio" is more common in the singular and the feminine "orecchie" is more common in the plural.