There are issues with credentials that you could solve by impersonation or elevating rights of the user the web app is running under.
However, we did it by adding the network printer as a printer on the server (add printer dialogue on server) and having the job sent to that printer.
We used the Printing.PrintDocument like so (Code in VB)....
Public Class SpecialReportPrintJob
Protected Overrides Sub OnBeginPrint(ByVal ev as Printing.PrintEventArgs)
Me.PrinterSettings.PrinterName = "PrinterNameUsedOnServer"
'setup rest of stuff....
'And we then call it like so
Dim printSpecialReport as new SpecialReportPrintJob()