No. You cannot first use a numerical integration to first integrate with respect to one variable, and THEN hope to use a symbolic integral on a second variable. The numerical integration produces a number. It will NOT be a symbolic function of y or any other variable.
Can you interchange the order of the integration? Yes, under some circumstances. As long as the limits of integration are not impacted, then you should typically be able to integrate on y first, and then use a numerical tool to integrate that result over x. And in some cases, even if the limits of integration are an issue, you may be able to resolve the problems. All of this would be specific to the case at hand however.