Can electrical devices such as inverters affect the communication with the MSF-01 sensors?

Yes this is technically possible. Although hard to evaluate the effect pre or post fitment interference to most wireless communications can come in many forms and electromagnetic fields from motors or inverters are some of those.

Many aspects of the environment can effect Bluetooth signals like magnetic/radio interference from equipment such as variable speed drives, cabinets or anything that might form a faraday cage around the equipment such as cabinets or guards. Moving the collection device closer to the MSF during collection will help overcome this.