Well, technically it could. There is nothing stopping the Michael addition product from being enolised and when enolised there is little to stop the enolate attacking a different carbonyl.
When I say ‘little’, that was a little lie, though. The main inhibiting factor is the Baeyer strain on three- and four-membered rings. These rings are rather strained (try building them with a molecular model kit!) and thus do not form easily. Especially, a nucleophilic attack onto the carbonyl carbon would be very difficult if not impossible to perform if it generates a four-membered ring. You can also try that with a molecular model kit, and remember that the nucleophile has to attack the carbonyl group in the Bürgi-Dunitz angle of approximately $107^\circ$.
In a regular Robinson annulation, as Ron described, the Michael acceptor system can be enolised on the ‘far’ side of the ketone — the one where your molecule has a phenyl group. It is then this enolate that attacks the other carbonyl group to form a six-membered ring — one that does not have Baeyer strain and is generally the most thermodynamically stable ring system. Your system cannot do this as it is lacking α-hydrogens on the ‘far’ side of the Michael acceptor.