How can Get-ChildItem be tested for no results (zero files)?

Try wrapping in @(..). It creates always an array:

$Files = @(Get-ChildItem $BackupPath_Root -include *.bak -recurse 
           | where {$_.CreationTime  -le $DelDate_Backup })
if ($Files.length -eq 0) {
  write-host "   no files to delete." 
} else {
  ..
}