With what Juraj said, if you're open to creating a user control you could do this in code with some XML and LINQ to XML. This should get you started:

CMS.PortalEngine.PageTemplateInfo pti = CMS.PortalEngine.PageTemplateInfoProvider.GetPageTemplateInfo("TemplateName", 1);
var doc = XDocument.Parse(pti.WebParts);
List<string> elements = doc.Descendants("webpart").Select(el => el.Attribute("guid").Value).ToList();

From there the elements List<string> object will have all the guid's of the webparts. Then you can create another List<string> and query the XML again but go a node lower to get the property name="transformationname", "selecteditemtransformationname", etc. and get those values.

So its not entirely impossible, but SQL isn't the option, you'd have to write some code.