Absolutely yes, it is possible for altcoin to grow without the influence of bitcoin, even several occurrence of such has happened numerous times. One of the time such happened around the Q3 of 2019 where most altcoin was growing more than bitcoin price. Also a spike in price of altcoin happens mostly when the team decides to list to the token on a top tier exchange. The hype around such exchange and the community members spirit brings about the increase in price.