No, even though you are over 18 you cannot drive alone without a licensed driver in the car with you if you have a New York learner's permit.

According to the NYS Department of Motor Vehicles no matter what age you are, if you hold a learner permit, you may not drive:

• Unless accompanied by a supervising driver at least age 21 who has a license valid for operating the vehicle you are driving. For example, only a person with a motorcycle license may supervise a motorcycle learner.
• In a DMV road test area.
• On any street within a park in New York City, or any bridge or tunnel under the jurisdiction of the Triborough Bridge and Tunnel Authority.
• On the Cross County, Hutchinson River, Saw Mill River, or Taconic State parkways in Westchester County.

Learner permits, limited-use junior driver licenses (Limited Class DJ or MJ), and full-use junior driver licenses (Class DJ or MJ) allow limited driving privileges for people learning to drive.

The NYS DMV states as a learner or junior driver, it is your responsibility to know and obey the restrictions. They have a publication for new drivers that lists restrictions and conditions for the different license types as a person goes through the NY graduated licensing process.