The moisture indicator is a means to detect excess humidity in shipping and storage. The leads corrode if exposed to moisture, so this is a good way to show poor storage ( stored in open packages, stored in high humidity in a warehouse, left in rain) which will make the product have poor solderability during manufacture.
The packages themselves are not totally impervious to water, and will slowly diffuse water vapour through, especially bad on a small SMT device where the actual die is barely under the epoxy, and where any voids will accumulate moisture, which can be bad if a lead wire or bonding pad is part of the cavity, as that will eventually corrode and go open.
Driving off the moisture will not help remove existing corrosion, but will keep it from spreading. Best is to store the units ( if you are going to store for period of 6 months or more) in the sealed original unopened packaging, and additionally place this in a further bag with a desiccant sachet inside as well, and check this at regular intervals for moisture ingress. With a mylar bag that has a waterproof lining, and properly sealed, this can last decades. I often got spares that had been stored for 40 odd years, still perfect with the desiccant showing no moisture, as military stored spares. These had been in a warehouse with no climate control other than a tin roof keeping rain off, exposed to temperature swings every day.