No.

To get down the hair from where you apply the heat, that heat has to be conducted down the hair, and hair is a very poor conductor of heat. That is why it keeps us warm (or cool).

To get some idea of how badly hair conducts heat, hold a wisp of hair in your hand and burn the far end of it (burning causes a far higher temperature than the straightener does) and see how close to your fingers you can get before you can feel any warmth from the hair.

Laser treatment to kill follicles heats the follicles far more directly, and even that doesn't generally work with just one treatment.

The straightener might weaken the hair itself by scorching it, but that is just dead tissue. What matters is the live tissue down in the follicle. When new hair grows out to replace the old, scorched hair, that new hair is as good as ever.

If you seem to be going bald or grey, that is for other reasons. 

Try to worry less.

Jon