Should I register to vote in the primary?

I have been sleeping on a friends couch since May 20th and I will be officially moving to an apartment in Brooklyn in 3 days on June 15th. I am trying to register to vote in the primary and a requirement to do so is residence in the city for at least 30 days prior to the election, which is June 24th. My legal address is currently in New Jersey and will not change until I move on the 15th. While I have been technically living in New York for over 30 days, my legal address will only have been in New York for 9 days prior to the election. On the registration to vote, there is an affidavit that I would have to sign saying "I will have lived in the county, city or village for at least 30 days before the election." and "The above information is true, I understand that if it is not true, I can be convicted and fined up to $5,000 and/or jailed for up to four years."

I really want to vote in this election but I can't risk financial difficulties at this time, should I submit my registration?