If contracts require delivery in BTC (supposedly this is how the ICE contracts will work), then I could see them affecting spot markets because it will be a legitimate avenue for investors/traders to buy actual bitcoins. That means real demand meeting real supply, and real arbitrage.
It doesn’t really matter whether the contract is cash settled or settled by delivery, as long as (this is a crucial assumption) you are able to execute a transaction in the spot market for the settlement price, at the settlement time. That is the reason why cash settled contracts exist. Think about it - it doesn’t matter whether I get 5 bitcoins delivered to me in the futures market, or X $, with which I can buy 5 bitcoins. The arbitrage trades still hold good.
You're making a big assumption with that condition (highlighted in bold). Sure, you could do that, if you can afford to trade CME contracts, and if you want a super inefficient way to accumulate bitcoins -- which still doesn't solve the spot market counterparty risk problem. The primary motive to trade regulated cash-settled futures is lack of counterparty exposure to unregulated spot exchanges. But that fundamentally means you're trying to profit from spot market moves (in cash), not move the spot market. CME traders aren't turning around and wiring their profits to Bitfinex, etc. That would be an outlandish assumption.