Technically it is possible to run BSEC from any compatible device, which doesn't have to be the same MCU/device that is directly connected to the BME680. On the other hand, all BSEC requirements must still be met, therefore:
The BME680 should still be configured as request by BSEC based on the selected operation mode (e.g. ULP, LP, etc.),
Timings should still be accurate and match the selected BSEC operation mode,
A valid timestamp is still required along with the raw sensor data when processing a sample in BSEC,
We would need some more details to check the compatibility of BSEC with your platform. Please share the complete MCU part number, the full compiler name and version, as well as any mandatory project settings or compiler flags needed (otherwise default settings) and we will review this option.