Yes it will affect the underlying price.
The two assets are linked quite strongly. If someone issues a futures contract, they’d need to hedge the risk by buying the underlying stock. In this sense a futures contract is priced exactly as a function of the underlying price plus cost of interest/carry.
So if you manage to buy enough futures contracts to make a significant movement in the futures price, you will also have forced a significant amount of stock purchase.
Even in the case where all the contracts you purchased were not newly hedged, the difference in futures/underlying means there’s now an arbitrage opportunity. So other market participants will see this and either long the stock or short the futures.
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