I don't have anything like this written, but it should be pretty straightforward.
You could either implement this as a macro, as an IExternalCommand that would show up in the external tools drop-down in the Add-ins toolbar, or implement your own button using an IExternalApplication and an IExternalCommand. Check the Revit SDK samples if you're not sure how to do this. If you're new to the SDK, the macro is by far the easiest solution.
Partial C# code that should more or less do what you're looking for:
View activeView = doc.ActiveView;
PrintManager pm = doc.PrintManager;
//To pick the printer, otherwise the Windows default is used
pm.SelectNewPrinterDriver("PrinterToUse");
//To set print setting, otherwise currently active settings will be used
//This code requires Linq to be loaded
pm.PrintSetup.CurrentPrintSetting = (from Element p in doc.PrintSettings where p.Name == "SavedPrintSetting" select (IPrintSetting)p).First();
//I seem to need this to make anything work, but try without it first
pm.PrintRange = PrintRange.Select;
pm.SubmitPrint(activeView);
