It is very common operation to weld threaded projection nuts and studs to parts. It is one of the most common fastener systems used in industry. Yes, weld a projection nut to the desired bracket. Spot welding a nut to a steel part could create obstacles due to the large surface area and mass of the nut versus the steel part. Projections on the weld nut eliminate this situation.
Projection nuts are available in many configurations:
PROJECTION WELD NUTS AND STUDS
Automated feed systems are available for the production of many thousands of parts. Standard machines and processes are available for processing nut and stud components.
References: RWMA – Resistance Welding Manual 4th Edition
AWS – AWS Standard C1.1, Recommended Practices for Resistance Welding