Lisa,
Here is a link to the Little Falls dam's water measurements.
It will give you a feeling for the river's level. Scroll down to the "Gauge Height, ft" section. Anything over 4 is high and 5ft is starting to get into some serious water. I won't fish the helipad area if the water is over 5ft at littlefalls and even that is pushing it. I was down there one day and the water was up and I turned around. Later that day a boy went in and a good Samaritan went in after him and both were lost. It's worth respecting that river. Especially since it involves scrambling the rocks.
I'm not sure which spill overs your are talking about, but most of the year that "canyon" that you walk through doesn't have any water on it, but if the fish can run up from the river and there is flowing water, there can be fish in there, but most of the little tributaries are just there when it's rained recently. I've bushwacked from Fletchers to Chain Bridge (it required waders) and that was some isolated area. There are a lot of little fingers of water that reach in and I felt like there hadn't been a person through there in ages. The best place to get access is at Fletchers. Hike up the river trail from the boathouse. The trail reaches the river after about a quarter of a mile and follows close for maybe another half mile. The further you go, the more rugged the trail gets.
There is little room for a back cast, the water is fast and the bottom rocky. Expect to spend more time retrieving your fly from a bush or tying a new one on after it gets snagged on a rock (you do want these flies to get down in the water column).
Carl