I don't really see any reason to use a silyl enol ether. The Michael acceptor is the pre-nucleophile and the aldehyde is the electrophile. If the aldehyde is replaced by a silyl enol ether, a nucleophile, the only way I see the Baylis-Hillman reaction happening is if it hydrolyses to the corresponding carbonyl in situ. In that case the mechanism would just be silyl enol ether hydrolysis followed by a normal Baylis-Hillman. Given it on paper, I would have predicted the silyl enol ether adding 1,4 across the Michael acceptor.
Masking the electrophile (aldehyde/ketone) as a nucleophile (silyl enol ether) does not seem to be sensible, because your nucleophile (Michael acceptor-amine adduct) is already masked as an electrophile (Michael acceptor). In other words, the pre-nucleophile (an elecrophilic Michael acceptor) and the pre-electrophile (a nucleophilic silyl enol ether) could react with each other.