PowerShellGet should automatically update PSModulePath on PowerShell 3.0
When you run Install-Module to install one or more modules from the PowerShell Gallery, by default those modules will be placed into %ProgramFiles%\WindowsPowerShell\Modules, yet on PowerShell 3.0, that path is not part of PSModulePath by default. That path only became part of the default PSModulePath in PowerShell 4.0 or later.
This is a big problem for PowerShell 3.0 because after a module is "installed", the commands within that module won't be discoverable and the module will not autoload without manual intervention (loading the module via the path or manual update of the PSModulePath environment variable).
PowerShellGet should address this problem by automatically adding %ProgramFiles%\WindowsPowerShell\Modules to the beginning of PSModulePath if it is missing and if the environment is running PowerShell 3.0. I just searched the PowerShellGet psm1 file in version 18.104.22.168 and couldn't find anything indicating to me that it does this today.
To see tested code that does this today and that is used to install modules hosted on GitHub, have a look at lines 95-119 in the Install-ModuleFromGitHub gist, which can be found here: https://gist.github.com/KirkMunro/131308abfb2d857bea40. It updates the appropriate system environment variable and PSModulePath in memory, placing %ProgramFiles%\WindowsPowerShell\Modules in the appropriate position in each of locations.