Yes, it is very possible that Jesus had in mind Ecclesiates 11:4-5 as He spoke the words in John 3:8, for the context in Ecclesiastes 11 supports His intention in John 3.
Ecclesiastes 11:4-5 (KJV)
4 He that observeth the wind shall not sow; and he that regardeth the
clouds shall not reap 5As thou knowest not what is the way of the
spirit, nor how the bones do grow in the womb of her that is with
child: even so thou knowest not the works of God who maketh all.
We must start in verse 4 which states that if a person is completely committed on observing solely the physical aspects of sowing and reaping to base their livelihood (ie, observing the wind direction and watching to clouds), they may lose their harvest because, as verse 5 states, God, through the spirit and supernatural processes, is the one who provides the increase at harvest time.
In John 3:8, Jesus applies the same rationale to the salvation experience.
John 3:8 (KJV)
8The wind bloweth where it listesth, and thou hearest the sound
thereof, but canst not tell whence it cometh, and whither it goeth: so
is every one that is born of the Spirit.
Jesus creates a metaphor where He uses the physical aspects of the wind to represent the Spirit of God. A person may look and see something happening as a result of the wind (eg, trees moving, air pressure on the face, etc) but you can’t see the physical processes that produce the wind. So, in like manner salvation is by the way of the Spirit of God. Everyone that is born of God is born by the invisible processes of the Spirit of God. A man may see the outward result, (eg changed life, changed actions, etc) but no can see the internal process that drives those results.
In both cases, Ecclesiastes 11 and John 3, scripture is saying that life (both physical and spiritual) is supported by God Himself through His Spirit and not through the work of man or by physical processes.