I was wrong. It turns out out that his independent status will not prevent his being on the ballot, though there is always the possibility that they will find a different way to ratf%$# his campaign:

Several New York politics blogs and publications have recently said that Bernie Sanders is in danger of being kept off the New York presidential primary ballot because he is not a Democrat and the Democratic Party has the power to keep non-members off its prseidential primary ballot. Here is the article in Power Line; here is the article in Gothamist. Here is the CapitalNew York story.

The articles are incorrect. The Wilson-Pakula law does not pertain to presidential primaries. The Wilson-Pakula law, sec. 6-120, does keep non-members off the primary ballots of parties (unless party committees approve letting them on), but it only relates to offices for which nominations are made. No state’s presidential primary nominates a major party’s presidential candidate. Only the party’s national conventions do that. The candidates in New York Democratic presidential primaries are individuals running for Delegate to the national convention.

My bad.  I was wrong.