There is no number for the progress stream, so you can not redirect it in classical way.
You can use the System.Management.Automation.PowerShell class to run your code.
Something like this
$code = @'1..10 | %{
Write-Progress -Activity 'Test stream' -Status "Counter $_" -PercentComplete ($_*10)
sleep 1
}
'@
$ps = [System.Management.Automation.PowerShell]::Create()
$ps.AddScript($code,$false)
$ps.Invoke()
$ps.Streams.Progress