Is it perfectly acceptable to take off a fitting and solder a coupling to it, as opposed to going back and soldering to virgin pipe?
Nothing wrong, except that it is more difficult to re-use a fitting or resolder to a length of pipe.
The solder residue from the previous time might be too bulky to fit the parts together.
For one reason or another, the joint made with re-used parts often develops oxidation inside during reheating and the solder doesn't seal the joint properly and it leaks.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.