Is this possible?

I think the real problem is that the solution isn't a workaround with general applicability. It happens to serve in the particular example used by the original poster, but it wouldn't enable the notation of consecutive chords with stems spanning both staves:

(Fortunately, it's never strictly necessary to use such a notation method. It would be a decision by an editor or an engraver, and my own preference would be to use ledger lines instead.)

Also, the workaround relies on the value of the note placed in the lower staff being a quarter note. If a note of shorter duration were used instead, its stem could still be lengthened -- but it wouldn't be possible to set the flag invisible independently of the stem.