Whenever I've done that route in the spring there was definitely water. If you get down to the Verde near the bridge, I think there are some fording points on the Verde actually. I know there are at the Verde at the end of the power line road. Now that Verde is running this year so be careful. Check the SRP lake and river levels and see what the inflow is to Horseshoe and Camp Verde and interpolate to where you are. There is a significant year round ford that is actually significant on the Bloody Basin road within a couple miles of I-17.
A really fun trip, if they still allow it, is Red Creek. Same exact area. Google it. Somebody else has to know if they still allow that route. In the early summer one year we did this route all the way to the Verde and where Red Creek empties, there is a really nice long sandy beach with lots of soft silty dirt. Because it is a fairly big confluence and so much emptying in, the river is nice and wide there.
You know what else is really fun? Take the rigs up Four Peaks and go over and down to Roosevelt. Not tough at all but gorgeous, really. There will be spots on the back side that are tougher. Then you could do a loop and go over the 'new' (new to me at least) bridge over Roosevelt and take the Apache Trail down past Apache Lake, Canyon, etc. Easy trail but very scenic. The Apache Trail is passable by Civics.
The Wilderness Area on the East side of Roosevelt is way, way, cool too.