No.
The W-3/ 1096 are the actual information tax returns needed to PAPER file 1099s or W2s for your employees. If you efile, this is not needed.
See our QuickEmployer Forms FAQ:
Do I have to e-file Forms 1096 or W-3?
Form 1096 and W-3 are not required for e-file. Quick Employer Forms only supports e-file with the SSA and IRS. Please do not send any of these forms to the IRS, as this will generate duplicate filings. These forms are simply for your records.
A follow up question- if I e-file the 1099's and W-2's do I need to send anything (1096 or W-3) to the state agencies?
Maybe. See the Quick Employer Forms FAQ's
"After e-filing, be sure to check your state's website for W-2 or 1099 reporting requirements. Each state's requirements vary, and most don't require the forms be submitted. Perform an Internet search for your state web address to find details. You do not need to mail anything to the IRS or SSA after e-filing with Quick Employer Forms."