Re-render a component after downloading a file

Question

I have the following code of commandLink:

<h:commandLink id="number1" immediate="true" value="Downloadfile" action="#{businessBean.downloadFileAsZip}">

And downloadFileAsZip method:

FacesContext context = FacesContext.getCurrentInstance();
ExternalContext eContext = context.getExternalContext();
HttpServletResponse response = (HttpServletResponse) eContext.getResponse();
response.reset();
response.setContentType("application/zip");
response.setCharacterEncoding("UTF-8");
try (ServletOutputStream out = response.getOutputStream()) {
    try (ZipOutputStream zOut = new ZipOutputStream(out, Charset.forName("cp866"))) {
    byte[] data =  ...some data....;
    zOut.putNextEntry(new ZipEntry("some file"));
    zOut.write(data);
    zOut.closeEntry();
    zOut.flush();
    }
}
facesContext.responseComplete();

I guess that it is impossible to download a file and rerender the page components within the same response. Is there a possible solution so that when the button is clicked, not only the file is downloaded, but also the jsf component with a specific id is updated?