I would definitely say "no" on this assumption, if this assumption was indeed correct, thus high liquidity leads to high volatility then Bitcoin and Ethereum would be some of the most volatile crypto assets in existence.
Some months ago I've written an article on how to correctly apply the use of correlations into crypto trading and hedging strategies:
https://open.substack.com/pub/nils89/p/the-importance-of-correlations-in?r=2qzuk0&utm_campaign=post&utm_medium=web