Find the Path for Excel-addin in Powershell

$Excel.Addins returns objects with more properties than just the Name, but that Name property is the addins Filename and includes the extension, like .XLL or .XLAM.

Another property you could probe is the .Title.

Try

try {
    $Excel = New-Object -ComObject Excel.Application

    $Excel.Visible = $false
    # you may also try Where-Object { $_.Title -match 'MyAddinName' }
    $myAddIn = $Excel.Addins | Where-Object { $_.Name -match 'MyAddinName' }

    if ($myAddIn) {
        Write-Host "AddIn '$($myAddIn.Name)' found in '$($myAddIn.Path)'"
        # copy the supporting file to the Addin's path
        Copy-Item -Path 'X:\YourSupportingFile' -Destination $myAddIn.Path
    }
    else {
        Write-Warning "Addin 'MyAddinName' not found"
    }
}
catch {
    Write-Warning "Error:`r`n$($_.Exception.Message)"
}
finally {
    if ($Excel) {
        # close and cleanup COM object
        $Excel.Quit()
        $null = [System.Runtime.Interopservices.Marshal]::ReleaseComObject($Excel)
        [System.GC]::Collect()
        [System.GC]::WaitForPendingFinalizers()
    }
}

^{This assumes there is only one addin found with that name..
Instead of the regex -match operator you could also use -like '*MyAddinName*' which uses wildcars}