Drill Wood Block Before or After Finishing?
You can finish first or drill first, your choice.

Drilling first then finishing will result in (at least some) of the varnish getting into the holes, which will not really add any value I can think of and perhaps cause you to re-drill the holes to the proper size prior to inserting the wood inserts and grommet.

The only drawback to drilling after finishing, that I can think of, is the potential to mar your nice new finish with tool marks. Solution(s) would be to let it cure thoroughly prior to drilling, so the surface is nice and hard, and/or to fine sand any tool marks and hit it with another coat when you're done.