Below code is Tested and Working Fine

http://soreddymanjunath.blogspot.in/2014/01/add-existing-list-webpart-to-page-using.html

Below Code Reads the SiteUrls from Text file called SiteUrls.txt, and add library called "Oct Invoicing 2014" to the Wikipage called "Billing_Req.aspx"

Here we are taking variable i to check for the library already present on the page, if present we are incrementing i to 1 and else its default value =0

If i=0 means webpart is not present on the page and it will be added on the page.

in All the cases we are writing the output to D:\Webpartoutput.txt.

cls 

asnp "*sh*"

$file=Get-Content -Path D:\SiteUrls.txt

foreach($url in $file)
 {

$web= Get-SPWeb -Identity $url

$listName = "Oct Invoicing 2014"

$pageUrl= $web.GetFile("SitePages/Billing_Req.aspx");

if($pageUrl.Exists)
{

    try
     {
  
    $i=0; 

    $webpart = New-Object Microsoft.SharePoint.WebPartPages.XsltListViewWebPart

    $list=$web.Lists.TryGetList($listName)
           
    $webpart.ListId = $list.ID
    
    $webpart.ViewGuid = ($list.DefaultView.ID).ToString("B").ToUpper()  

    $webpartmanager=  $web.GetLimitedWebPartManager($pageUrl,[System.Web.UI.WebControls.WebParts.PersonalizationScope]::Shared)

    foreach($wpt in $webpartmanager.WebParts)
    {
     
         if($wpt.ListId -eq $list.ID)
         {
         $i=$i+1;
         break;

         }
    }

    if($i -eq "0")
    {

        $webpartmanager.AddWebPart($webpart,"",0)

       "Webpart Added Successfully" + $url + " " + $webpart.Title |  Out-File   -Append -FilePath D:\WebpartOuPut.txt
     }
     else
      {
         " Dude Webpart is already present on the site  : " + $url |  Out-File -Append -FilePath D:\WebpartOuPut.txt 
      }
  }
 
  catch [Exception]
      {

   $url + $_.Exception.Message | Out-File -Append -FilePath D:\WebpartOuPut.txt 
     }
    }
          else
    {
    "Page Url is invalid or not existing  : " + $url  | Out-File -Append -FilePath D:\WebpartOuPut.txt 
    }
 }