Is 'Snapped' Onomatopeia ?

No. The etymology of the word will tell you that the origin came from the Middle Low German/Middle Dutch 'snappen', which meant 'a quick, sudden bit or cut' - an action, not a sound, and it may have been derived from the word for beak or bill, 'snavel', which itself is believed to be based on West Germanic imitative root 'snu', used with words pertaining to the nose (snout, and probably the later Yiddish 'schnozz').

Not quite. It's one of the "sn" words that's somehow connected to the nose: snip. snipe, sniff, snore, snoot, snort, schnozzle. The sound of a sniff or snort might be the underlying onomatopoeia in all of them.