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Can heavy demand for options drive up or down a stock price?
You will tend to find as options get closer to expiry (within 2 months of expiry) they tend to be traded more. Also the closer they are to being in the money they more they are traded. So there tends to be more demand for these options than long dated ones that are far out of the money. When there is this higher demand there is less need for a market maker to step in to assure liquidity, thus there should be no effect on the underlying stock price due to the high demand for options. I would say that market makers would mainly get involved in providing liquidity for options way out of the money and with long periods until expiry (6+ months), where there is little demand to start with and open interest is usually quite low.