You can wrap the following instructions with a GuestOps RunProgramInGuest call.
Others have also created custom installation scripts for VMware Tools that you can invoke as well.
Without VMware Tools, you won't have access to the GuestOperations API and your VM may not have proper drivers for network connectivity. For this reason, VMware Tools are usually baked into Templates and deployed by cloning and customization. However, if you can run some remote scripting execution, you can execute the remote installation process and reboot your VM.
For example, you could create a custom ISO image with the automated installation command in a batch file. Then use WMI to remotely execute it (may be some permission issues, been a while). May also be possible to use the autoplay functionality, though I know that has some caveats that may prevent an automated install. I have some customers who run an SSHD instance on their Windows VMs for consistency between Linux VMs for remote automation.
Linux is a similar process, but you may want to rebuild your tools package and pack it into an RPM or DEB file for simplicity of install.
Most tend to incorporate the tools installation process into their OS build process or templates. However, with a little automation and the right permissions you can remotely install them as well.