Q:

Is there a way to check if the site that we are migrating has any infopath forms in it?

Is there a way for us to find the list of lists/libraries that use Infopath forms in a SharePoint site?

A:

Yes, we can.
Using the below PowerShell script, we can get all infopath forms from a particular web application and this report will be exported to a csv file.
[System.Reflection.Assembly]::LoadWithPartialName("Microsoft.SharePoint") > $null 

function global:Get-SPSite($url){ 

    return new-Object Microsoft.SharePoint.SPSite($url) 

} 

#Get the web application 

$WebAppURL= "<Web Application URL>" 

$SiteColletion = Get-SPSite($WebAppURL) 

$WebApp = $SiteColletion.WebApplication 

#Write the CSV header 

"Site Collection `t Site `t List Name `t List Url `t Docs Count `t Last Modified `t WF Count `t Live WF `t Live WF Names `t Form Template" > c:\temp\InfoPathLibs.csv 

#Loop through all site collections of the web app 

    foreach ($site in $WebApp.Sites) 

    { 

       # get the collection of webs 

       foreach($web in $site.AllWebs) 

        { 

            write-host "Scaning Site" $web.title "@" $web.URL 

               foreach($list in $web.lists) 

               { 

                   if( $list.BaseType -eq "DocumentLibrary" -and $list.BaseTemplate -eq "XMLForm") 

       { 

                  $listModDate = $list.LastItemModifiedDate.ToShortDateString() 

                $listTemplate = $list.ServerRelativeDocumentTemplateUrl 

                  $listWorkflowCount = $list.WorkflowAssociations.Count 

                $listLiveWorkflowCount = 0 

                $listLiveWorkflows = "" 

                foreach ($wf in $list.WorkflowAssociations) 

        { 

                    if ($wf.Enabled) 

         { 

                        $listLiveWorkflowCount++ 

                        if ($listLiveWorkflows.Length -gt 0) 

         { 

                            $listLiveWorkflows = "$listLiveWorkflows, $($wf.Name)" 

                        } 

                        else  

         { 

                            $listLiveWorkflows = $wf.Name 

                        } 

                     } 

                 } 

       #Write data to CSV File 

                   $site.RootWeb.Title +"`t" + $web.Title +"`t" + $list.title +"`t" + $Web.Url + "/" + $List.RootFolder.Url  +"`t" + $list.ItemCount +"`t" + $listModDate +"`t"  

+ $listWorkflowCount +"`t" + $listLiveWorkflowCount +"`t" + $listLiveWorkflows +"`t" + $listTemplate >> c:\temp\InfoPathLibs.csv 

             } 

               } 

        } 

    } 

#Dispose of the site object 

$siteColletion.Dispose() 

Write-host  "Report Generated at c:\temp\InfoPathLibs.csv" -foregroundcolor green 

Note:
In the above code $list.BaseTemplate -eq "XMLForm" indicates that this list has been modified in infopath form or type of infopath form.
Reference URL:
Find all lists that have an InfoPath form

