Yes. It can be done. But only by a specific amount unless you buy some special replacement bushing.
Under the nozzle is a bolt that goes through a plastic bushing. This bushing is oval in shape and has an offset hole that is typically set up so the hole is farther back towards the stern. This makes the nozzle point upwards to some degree. You can take out the bolt, take out the bushing, flip it and reinstall. This will point the nozzle down to some degree.
Now, with that being said, if you do this, you will encounter other issues.
1. You now need to re-adjust your bucket position considerably. Now that your nozzle is lower, you need to make the bucket drop farther down.
2. Because you've had to adjust your bucket down, it will no longer latch correctly when it's in full forward position. I'm not sure how to fix that (or if it's possible). The plate the bucket latches to is fixed permanently in a specific spot.
3. The angle of your boat at running speed will change a bit, but it's pretty minor.
I purchased my boat second hand, it came with the nozzle down. I ran it that way for 3 summers not knowing until my bucket finally dropped down once at speed. It caused the boat to submarine dramatically with water going over the boat everywhere. It was pretty scary. That's when I discovered what had happened. I put it back myself and adjusted things. Bucket now latches so that this doesn't happen again. I can't see how you could drop the nozzle and still latch the bucket. It may not cause any issues... but having experienced it, I would vote not to do this.
At the source, are you having problems steering? It took me some time, but I've never felt a need to add extra stuff to help with that. But then again, I have a small boat.