The changes to the main data area itself are usually not written immediately, but later on to optimize disk access. If there is a power failure, the main data area is not up-to-date, but because the changes are in the transaction log, the changes are re-applied automatically the next time the database is opened.
However, there are cases where the H2 DB server may crash due to OutOfMemory reasons and corrupt the whole db. In such a case a full recovery of the H2 DB needs to be performed.