Well, I would not expect any miracles here because a cold oil is several times more viscous than when it is up to the operating temperature. You may get a little bit of improvement, but I would not expect much.
If your pump is worn out, it will need to be replaced eventually.
I would probably try cleaning it first. Maybe use an engine flush in it and see what happens. After that I would try to use something thicker, but I would start budgeting for a pump replacement. Maybe find a place that rebuilds them? In America we are a throw away society and hardly anything gets truly repaired here, but your place might be better in this regard.
