No, as psexec evoke a cmd prompt remotly via psexecsvc.exe to run the command, thus need access to admin share for the first handshake.
To quote how it work;
How Does PsExec Work?
In the resources of the executable file PsExec.exe, there is another executable file – PSEXESVC, which is a Windows service file. When establishing a connection to a remote computer, the PsExec utility copies this file to the hidden administrative folder Admin$ of the remote computer (C:\Windows\System32\psexesvc.exe). In order for PsExec to connect to a remote computer, the LanmanServer and LanmanWorkstation services must be running on a computer. The SMB port (TCP/445) and UDP/137 ports should be opened on the firewalls between source and target computers.