Yes: as I said, supplementary relatives (unlike integrated ones) can have virtually any element as antecedent including verb phrases.
Coincidentally, I came upon a supplementary relative clause with a verb-phrase antecedent today in Charlotte Brontë's novel
Jane Eyre. It's in the first sentence of Chapter 20:
I had forgotten to draw my curtain, which I usually did, and also to let down my window-blind.
-- Charlotte Brontë
The antecedent of
which is the verb phrase
draw my curtain.
P.S. Regarding Trump's Tweet, I continue to have issues with the interaction between the negation in the clause of the VP antecedent and the supplementary relative clause. I have checked all my major grammar books (Quirk et al. 1985, Huddleston and Pullum 2002, Curme 1931, Sweet 1898, Poutsma 1916) and cannot find a single example in which negation is used in the clause containing the antecedent of such a supplementary relative clause. I take this as a sign that I might be right that it's "bad." However, no one seems to actually say that it is. At a different site where Fujibei also asked this question, someone has (for better or worse) linked to the following paper -- which is
not for learners:
http://www.ling.uni-potsdam.de/~thiersch/RelCl/borsley_4178997.pdf
I haven't had time yet to read the paper. But on page 645 (page 18 of the pdf) there is a footnote with the following example:
(i) John was sent to Manchester, which I have never been.
There we have negation in the supplementary relative, but not in the clause with the past-participle VP antecedent. I wonder what my fellow native speakers here think of the following variation, which flip-flops, Trump-style, the negation scenario.
(i-a)
? John was not sent to Manchester, which I have been.