No, if you depart from the United States before your Advance Parole is approved, your application for an Advance Parole Document will be presumed abandoned.
Also, if you are an adjustment of status applicant whose Form I-485 is still pending, and you decide to travel outside the USA without an Advance Parole, your case will be considered abandoned and denied accordingly.
Meanwhile, please note that leaving the USA, even with an Advance Parole, may impact your ability to return. DHS will make a separate discretionary decision whether to parole you each time you use an Advance Parole Document to return to the United States. And you may not be permitted back into the USA in case you are found to be inadmissible. DHS may revoke or terminate your Advance Parole at any time, including while you are outside the USA.