" Our sink is not installed yet so it can be take out for the cabinet finisher to stain the drip edge. "

100% have that finished before tops. In fact it is probably best to have the cabinets all finished before the tops.

You're not getting that much water down the front of the sink to worry about.

We have had a farm sink like this for 7 years and have never had water run down the front. I cannot imagine a normal situation where that would be necessary. Also leaning against the sink, that edge would irritate me.