Most modern phrase structure grammars will assume that the string immediately after an inverted auxiliary is the complement of the auxiliary, as the question implies. This fact is largely due to the assumption among these grammars that all syntactic branching is binary. If indeed all branching is binary, one has no other option but to view that string as a constituent and hence as the complement of the auxiliary.
If one is willing to acknowledge ternary branching, though, then one can easily position the subject and the non-finite verb phrase as sibling dependents of the auxiliary, as shown next:
This analysis views the entirety as an auxiliary phrase, which means that the auxiliary verb is construed as the head. The subject he and the verb phrase leaving soon are, then, sibling dependents of the auxiliary. Such analyses were likely to occur back in the 1970s before the desire for strict binarity of branching in all cases led the mainstream syntax community astray.
In the type of grammar I prefer, which is a dependency grammar (DG), the sentence structures are flatter (in part because one assumes dependency rather than phrase structure as the underlying principle of syntactic organization). The dependency analysis of (1) that I prefer is along the following lines:
If one is used to phrase structure trees, which most linguists and students of linguistics are, then this dependency analysis might seem strange – in part because its so simple, just four nodes in the structure. It is, though, in a sense isomorphic with the phrase structure analysis in (1), for it can be automatically translated directly to (1) -- and similarly, the phrase structure analysis in (1) can be automatically translated to the dependency analysis in (2). The key insight in both cases is that the subject nominal and non-finite VP are sibling dependents of the auxiliary, which means they together do not form a constituent. For discussion of subject-auxiliary inversion (and inversion more generally) from a DG perspective, see pages of 216-220 in my book on DG: https://www.jbe-platform.com/content/books/9789027262288. I can connect you up with an electronic copy of the book if you contact me via email: [email protected].
There is an observation that strongly supports the flat analysis. This observation is that nothing ever intervenes between the auxiliary and the subject in such cases. For instance, it is impossible to separate the two with an adverb, e.g. * Is really he leaving soon?. The adverb can, though, appear immediately after the subject and before the non-finite verb, e.g. Is he really leaving soon?, which indicates that the subject nominal and non-finite VP do indeed NOT form a constituent, meaning that the flat analysis is well-motivated.
The example sentence in the question receives the following DG analysis:
Alex B commented that Croft’s Radical Construction Grammar likely does not view the string immediately after the auxiliary as the complement of the auxiliary. Alex is probably right. Be aware, though, that Croft rejects most syntactic tree analyses outright. He views constituent structure analyses as dubious from the start. His approach is hence rather nihilistic in this regard and is therefore indeed “radical”.