Unemployment question- New York

Hello-
I had a touch base with my boss a few weeks ago because she was leaving the company. I let her know I did not think the position I was in was a good fit for me and asked if I could use her as a reference if I found another job. She let someone higher up know who was training the new manager. We had a conversation and he said he will give me time to attend interviews and present me to positions we were working on (I work for a staffing agency) I was not expecting them to find a replacement for me right away. They let me know they had someone who could start, but can not keep both of us, so they are giving me two weeks to assist in training him and wrap up with my clients. Though I said I was looking to pursue other opportunity's, I never actually gave a notice. Would I be able to collect unemployment benefits if none of these jobs I interviewed for pan out, or am I out of luck?

Thank you.