See slide 14 here: https://transition.fcc.gov/oet/ea/presentations/files/oct09/ModularTransmittersReview_%20Oct09_JD_TH.pdf
- Your device has a transmitter that has modular approval
- There are no other transmitters in the product (see other notes in deck about combining multiple modules)
- You label the final product with the modular approval ID
"Except for RF exposure and radiated power and/or radiated emissions, additional equip. auth. not needed"
So you'll still need to meet SAR regs (if the product is used anywhere near a human body), and still do radiated emissions testing (ie part 15B), but you don't need additional equipment authorization.
You will certainly fail 15B if you have ANY transmissions, because you'll exceed the unintentional radiator limits... because you have a transmitter.
If you have bad harmonics from non-transmitting parts of the modular transmitter then you probably fall foul of the "Original module test data represents same characteristics in final product" note on that slide - ie you've made the original module behave worse than the test data suggested - and you know this, as you've done testing so you can't exactly plead ignorance.
From what I can see, Particle are not actually testing STM32+cell (someone correct me if I'm wrong?) but rather just quoting the modular approval of the uBlox module. If that's the case, it's quite possible that the Electron might fail 15B from the STM32, which implies that the modular approval is not applicable.
When you next go to the lab, can you take another particle-supplied board (eg asset tracker?) and see what the emissions there look like? You won't be able to improve over what the actual Electron emits by itself....