The volatility of Bitcoin has led to the shift in engagement because the price of Bitcoin can sometimes determine engagement. Like the economic variables; demand and supply. An increase or decrease in price, can lead to n increase or decrease in demand, conversely an increase or decrease in price can also lead to an increase or decrease in supply. From the aforementioned, one can say, the demand and supply can influence the price of Bitcoin. Can more adoption and engagement influence the price of Bitcoin as at a particular date?
General economics will make you understand that demand and supply is the foundation and root of every thing you see in the economic space, and this includes both trade and investments both physically or even digitally, the amount of demand affects price and supply and this is very much applicable to Bitcoin and other digital assets and just to quickly answer you question in the last statement, YES more engagement and adoption will affect the price of Bitcoin just like we saw some months ago when the US elections were concluded and the president did promised to get a Bitcoin reserve for the country and many person scribbled around to get some units of Bitcoin so the can benefit from the volatility that will arise due to the huge demand the US will be creating.
If a whale investor ask to buy Bitcoin now, it will cause a price surge because that will increase the demand because they will be buying in large quantities which will cause a good mop up from the market mostly from some very small scale retail traders as at the time. the reverse happens when a whale happen to sell off their asset too in the market'