As far as I know ICOs do contribute to bitcoins price because when investors buy tokens in a project that's running a token sale for a period of 2 months for example and lets say its raised 1000 BTC, this means amount of bitcoins in circulation is temporarily reduced in this period which will also force the value of bitcoins to raise provided demand is there.
I don't think ICOs can make it fast but forks is one of the reason why the bitcoin price rise that fast. Everytime a fork/hardfork planned in the next 2-4 weeks, the price of bitcoin always pumped so high. It's because the high demand of people are buying bitcoins to get freebies after the fork.
agree, people what a bag full of free airdropped coins that come from a fork