It depends on the application, but in general, yes, you have to be an administrator to install applications.
You may want to invest in Remote Desktop management software. You can then install software remotely without being physically present at the computer (.pkg anyway.) If you run into Installer VISE or ZeroG installers, you have to copy the installer to the computer, then remote control it and run the installer for the user. Otherwise, when dealing with packages, it's seamless and runs in the background.