You can I have done this the last two years. The problem is that downriver a few miles it gets real shallow, to the point I could not take my boat through. Most of the river near the falls(most) is fairly shallow under 10 feet or so. Now that being said there are a few deeper holes, and we caught some sturgeon also. What I found is that the sturgeon we caught were on the smaller side. I am sure there are some bigger ones, but we have not found any larger ones yet.
We fished that area the end of March both years, so maybe the water is higher this time of year