Meh.. Binance only has about 10% of the volume Bittrex does
But sometimes, good news about listed to new exchange can helps the value of token increases. Like Monaco, just before listed on Binance exchange, it had increased from @30k sat to @440k sat after 10 days

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Monaco announced the possible support the Visa. So the effect from Binance was mixed and there is no need to rely on it. At the price it really will affect but not as much as you write