Yes they probably do, particularly if the female produces eggs right before the frost. This behavior isn’t only observed in mantids in fact the death of a female soon after laying eggs is pretty common in the insect world. No wonder, praying mantis are pretty infamous for exhibiting some of the most bizarre behavioral adaptations. For instance, the female (though only occasionally) eats the male during mating.
Similarly the female mantis doesn’t only cannibalize her mating partner it also dies soon after laying eggs. However, this particularly behavior isn’t only limited to the praying mantis. Many bugs such as honey bees also die after producing eggs. Honey bee dies because its genitals explode. Perhaps this is a necessary part of an insect’s life cycle. Small mantis species live around 2 to 3 months and it’s reasonable to assume that their shorter life span might be due to this behavior.