Will removing the ecm fuse cause problems?

Will removing the ecm fuse cause problems?
Since the ecm (engine control module) is necessary to run a modern car, the simple answer is:
Yes.
Not having the year, make or model, exactly what the ecm controls in this instance is unknown. But regardless, the vehicle will not operate without it.

Also, removing the fuse and therefore removing power from the ECM may cause all the learned engine parameters revert to their initial state and your engine may not run as well or get as good mileage until the ECM relearns new parameters.