It's possible, although I think that will be more prevalent in places like New Hampshire or California.
People here need to be registered party members, so unless you decided to reenroll in a different party a year in advance simply to meddle in its nominating process this shouldn't really be an issue.
Are independents allowed to vote in major party primaries in New York? Or do you have to be an already registered Democrat or Republican to vote in the respective primaries?