As suggested in this article, the evolution of the adaptive immune system didn't actually give vertebrates a huge benefit, it just led to an escalation of the arms race between vertebrates and pathogens. As a result, we cannot survive without an adaptive immune system anymore.
One can then ask what would happen if we were to create bio-engineered insects with an adaptive immune system in the lab. If a similar escalation between the pathogens and the immune system would take place, then ordinary insects outside the lab would also be affected. But these ordinary insects would not be able to evolve an adaptive immune system before being wiped out. So, it seems to me that all invertebrates, except those we keep in the lab would die.