Do you think the PJ would have solved the case?
Given what happened with Tannerman, the short answer is no.
Now for an explanation.
On the 4th May, a chunk of the Smith family were occupied getting to Faro airport for an early flight to Ireland. They had not, by that time heard of MBM, nor of her appearance.
The PJ focus on 4 May was on getting 'proper' statements from the T9. I can't remember if other elements had started working their way through OC employees.
The normal PJ approach was not to go public with case details. A description of Tannerman took a long time to emerge. A drawing of Tannerman took even longer.
The PJ does not appear to have checked the creche records. There is no diligence in the PJ Files for this, and no copy of the creche records.
I've got no idea whether Smithman was a local or a visitor. For all I know, Smithman went to Ireland on the same flight as the Smiths. Or he went to Lisbon or Porto. Or he remained in Luz.
The PJ did not construct or publish the e-fits. I don't know if they went public with his description. The PJ have no capability comparable to Crimewatch.
Hopefully that explains my 'no'.