Will the economic model fitted using the data that is converted from Annual to Quarterly with the technique of "Quadratic Match Sum Process" have any drawbacks?
None, you don't gain more information, worse, you could produce an artefact. In this way, you could artificially gain degrees of freedom and use a more sophisticated econometric tool. But, it is not the good way. A better way would be o use quartely data correlated to your annual data and produce your own quarterly data.