Hi Logan,
Thank you for choosing AkrutoSync.
Yes it will. All previously sync contacts and calendars will remain on the phone even if it is not connected to your cellular network or Wi-Fi network.
You can try out the software and see if it works for you. You can download the 7-day free trial here:
https://www.akruto.com/get-akruto-sync/
Regards,
Brian Tan