Is John 3:16 the gospel?

No. This verse depicts the Kingdom gospel and not the Grace gospel. The gospel is absent in this verse and therefore one cannot use this verse as a basis to present the gospel to someone. Why not? This verse lacks the information that one needs to know regarding the death, burial and resurrection of Jesus Christ and what that purpose is for us.

John 3:16 is essentially the Kingdom gospel and had to do with the identity of Jesus Christ, and Jews [at the time of John's writing] had to acknowledge Jesus as their Messiah, (see John 20:31, Luke 12:8, Matthew 16:16, John 11:27).

The Grace gospel today is not about the identity of Christ, but rather with the cross work of Jesus; not who He is, but what He has done. For examples of the grace gospel, see 1 Corinthians 15:1-4; Romans 4:25; 1 Thessalonians 4:14; Romans 14:9; 2 Corinthians 5:15.
 
(Note, these scriptures above reference the cross work of Jesus, but it is advisable to provide more detailed explanations of these scripture to the intended person(s). Remember that you are communicating the message, but it is God's work, through the Holy Spirit that with bring the person to conviction. Conviction and salvation is between that person and God. You cannot force that person into a conviction. Just share the gospel and leave the rest to the Holy Spirit.).