How to mix parmessan (or any hard cheese) into oil sauce
It's not traditional to add cheese to fish dishes in much of Italian cuisine. Historically, this may be more closely connected to economics and religious beliefs than for any culinary reason.  As far as flavor development goes, if you like parmesean cheese with your fish based pasta dishes, by all means, use it.

Getting the cheese to emulsify into the sauce is quite tricky.  Even though it is an oil based sauce, you will typically need to add a bit of the pasta cooking water to help with the emulsification.  Also, you will want to remove the sauce from the heat before the addition of the water and cheese.  

When the pasta is about 1 to 2 minutes from being completely cooked, remove from boiling water directly to the pan with the condiment.  Add a few splashes of cooking water and stir vigorously to emulsify.  Remove from heat.  Add a bit of cheese, stir vigorously...and a splash or two of pasta water.  Continue until you have added all of the cheese, but a little at a time.

Sometimes, if it's too hot, or I don't have room in the pan to really stir and toss, it clumps.  It takes some practice and patience.