In a non-searchable and potentially ephemeral comment to the original posting, John Lawler presented the following answer:
Yes, but it’s very complex and convoluted syntactically, and will take anybody some time to parse.
And, given the current degree of grammatical knowledge among English speakers, about half would judge it ungrammatical anyway, or at least fail to parse it correctly.
Better space it out with a transformation, like Extraposition, or two. It’s only a rhetorical question, after all, and rhetorical questions are sposta be easy to understand.
I’ve marked this posting Community Wiki because it is John’s answer not my own, and so I deserve no reputation from it.