I don't think you can print PDFs with VBScript alone. However, SumatraPDF should be able to do what you want. It's a standalone executable and you can print PDFs to the default printer using the -print-to-default
option:
filename = "C:\path\to\some.pdf"
Set sh = CreateObject("WScript.Shell")
sh.Run "sumatrapdf.exe -print-to-default """ & filename & """", 0, True
See the manual for more details.