Should this be written with exception handling instead of nested if-thens?
Maybe simple loop logic can serve your purposes better. If what you want is to ignore the rest of the loop body if a condition is met, the continue statement will follow immediately with the next iteration.

foreach (string fileName in updateList.fileNameList())
{
    updatesForFile = updateList.updatesForFile(fileName);
    hyperlinkEntry = hyperlinkList.getHyperlinkEntry(fileName);
    if (hyperlinkEntry == null)
    {
        updatesForFile.markResultAllRows("File not found on server");
        continue;
    }
    hyperlink = hyperlinkEntry.hyperlink;
    if (updatesForFile.updateNeeded())
    {
        if (!po.checkout(hyperlink))
        {
            updatesForFile.markResultAllRows("checked out to other user");
            continue;
        }
        downloadPath = downloadFolder + fileName;
        downloadResult = dl.download(hyperlink, downloadPath);
        if (downloadResult == false)
        {
            updatesForFile.markResultAllRows("download failed");
            continue;
        }
        file = new FileObject(xlApp, downloadPath, updatesForFile);
        if (file == null)
        {
            updatesForFile.markResultAllRows("unable to open");
            continue;
        }
        foreach (FeatureUpdate featureUpdate in updatesForFile.getFeatureUpdateList())
        {
            resultValue = featureUpdate.getColumnValue("result");
            if (!resultValue.Contains("updated"))
            {
                file.update(featureUpdate, updateMethods.lowFeatureLength);
                updatesForFile.markResult(featureUpdate.getIndex(), "updated");
            }
        }
        file.close();
        updateList.save();
    }
}


If what you need is to exit altogether when a condition is met, then I'd favor return, maintaining the same logic as the continue example. This would also give a lot more flexibility to refactor your code into functions and even probably use of kind of error codes, if it gets to that point.

Exceptions are very useful, but they are very expensive, so unless you don't really care about the performance of this code, I'd favor a solution based in flow control any day of the week.