Put in conventional oil once. Run it a few hundred miles. Look for leaks and loss of (burning) oil. You can't go by what came in it when sold to you, might just be high viscosity goop meant to quiet the engine.
Anyway with the correct conventional in you have a baseline. If seals are leaking, switching to synthetic will probably make it worse with all else equal, but you can use high mileage synthetic with seal conditioners.
If the seals are not leaking with conventional oil, do not put high mileage conventional or synthetic in. It does nothing good for seals until they start leaking.
If you switch to synthetic and THEN it starts leaking, I'd top it off with high mileage oil and switch to 50% high mileage oil on the next change, not using more of the stuff than needed to keep leaks under control.
Shorter answer: Sure it's a good idea to switch to synthetic but don't try to drop down to 5W-20 because the engine is designed for 10W-30 or thicker.