Sorry papa - you didn't say the teak was already removed. I meant no disrespect to your question. However, if I was doing this, my choice would be to sand the removed teak articles prior to bedding, fastening and bunging. Then sand the bungs flush, mask and apply the required number of coats.
If you refinish prior to mounting, there is no way to effectively
varnish the sanded plugs to match the pieces already finished. I also think leaving the holes unplugged, with bare screw heads, would look rather undressed.
Just my opinion.