It probably can, if you are sure they are not weep holes. Personally, I would not do it. If pin holes have developed in the housing, imagine what the impellar may look like. You will feel much better, if you replace the pump--many come with a lifetime warranty. It sounds like the coolant has not been changed every 2 to 3 years.

I agree, its like plumbing, if a pipe has a pin hole the entire wall of the chamber is very thin and will go when you need the car the most.

I agree with my esteemed colleagues.
You could be treating a symptom but ultimately hiding a larger problem. Those pinholes could mean advanced corrosion from inside the cooling system.
What do the other system components look like? Any problems with them?