Does not rain much in Los Angeles, but I am thinking on welding shut the top of the cowl so no water gets thru there...

 

By law you have to have the heater. The DOT requires a defroster as part of the safety equipment, along with seatbelts, lights, turn signals etc. If you don't have a defroster even when it's cold outside, just your own body heat and breath can create window fogging, and if you get in an accident as a result you'd be screwed.

 

Personally, I would leave the heater alone except for repairing it. There may come a time when you want the heater or defroster to work. Also, In the event that you have to sell, the buyer may be less interested if these things have been removed.

If the cowl leaks you can temporarlily get a cowl cover.

I have one that I use just so leaves and other crap doesn't get in there.