When a penalty is accepted with less than two minutes remaining in either half, the offended team will have the option to start the game clock on the snap?

Yes that is "True".

In 2017, the NFHS Football Rules Committee embraced Rule 3-4-7 which gives an offended group the alternative to begin the clock on the snap when a penalty is acknowledged with under two minutes left in either half. This option applies to any accepted penalty by either group if the clock would otherwise start on the subsequent ready-for-play signal.