Unfortunately, no. VoteFromAbroad (VFA) helps you fill out the Federal Post Card Application (FPCA)–but you must submit your completed FPCA to your Local Election Official (LEO) in the U.S. Only your LEO has the authority to approve your FPCA and send out your ballots!
Using VFA, you may elect to sign your FPCA electronically and–if your state allows it–email it to your LEO automatically. Or you can print out your completed FPCA, sign and date it, and then Fax or Mail it to your LEO. All contact information for your LEO is in the Instructions included with your completed FPCA, as well as here. For a more detailed explanation of how to submit your FPCA, please see FAQ #5 (“How Do I Register To Vote Or Request A Ballot As A U.S. Citizen Living Abroad?”)