So when you die and rebuy (using insurance, this game's respawn mechanic), will rebuy clone your existing modules or will it only give you basic versions which you need to mod again using engineers?
Yup, it works, just tried it myself with enhanced drives and a modded fsd (grade 1 mod), just sell the modules before selling or changing ships and it will work
You can also transfer modded modules to other ships like pre-2.1 by selling them from one ship and rebuying them from the other ship. Tested this with a modified pulse laser yesterday.