Does $BNB burn has significant impact on price action?

Based on trend for past 1 year (2020), not really.

But, based on performance for this Quarter...
1. Yesterday (12 Jan), Binance Spot recorded ATH trading volume of 26B, compared to $424mm 13th Jan last year – a 65x increase
2. Which also means Binance is generating more than 26M in single day revenue.
3. Trading volume has increased significantly for this Quarter.
4. Overall for this Quarter, Binance revenue has been up more than 2x (Q4 2020 $3,500,767,911 vs Q1 2021 $7,240,280,387).
5. Which means the burn this coming 18th Jan will be roughly 2x compared to the previous burn, i.e. round 4.5mm BNB will be burned.
6. About 2.5% of BNB will be taken out from circulating supply permanently.

Yes. The impact will likely be noticeable this round.