Is this a correct way to tie together the passage about Moses and the serpent with the John 3 passage?

Joh 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
God loved the children of Israel, and gave Moses a serpent to lift up, that whosoever believed and looked to the serpent, wouldn't die, but lived.

Joh 3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
God didn't send the serpent into Israel to condemn them, but that they might be delivered from the effects of the serpent bite.

Joh 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
Those who believed and looked to the serpent, didn't suffer the consequences of the serpent bite, but lived. Those who didn't believe and didn't look to the serpent, already had been bitten by a serpent and therefore died, because they didn't believe God and look to the serpent.

Is it true that Jesus isn't really talking about why some believed (as in either some chose to believe or God changed their heart so they believed) so much as He's just 'stating some facts'.

God loved the world and sent Jesus. Some believe(d) and lived, others didn't/don't believe and die.
God loved Israel and sent a serpent so that they might live. Some looked and lived, others didn't look and died.

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B.Howes
Framingham, MA