Just because there is an opening for one species does not mean you can target other species that are not open. If there is an opening for crab it doesn't automatically mean you can shrimp or target halibut; same on a river. The openings depend upon the health and breeding cycle of the species in question and not all populations in the same water are equally healthy or at the same life cycle stage. Plus in that river, the only reason chinook are open is that they are surplus hatchery fish not needed by the hatchery a few miles upstream. Most other fish in that section of river are ESA-listed, so no, you can't target them.
Only part of the river is open for trout. The lower river from the mouth to the Leavenworth hatchery rack is closed for everything except Chinook. (Translation, the pamphlet says it is closed for all species but there is an emergency opening for chinook but this does not mean that you can also target steelhead, coho, bull trout or anything else)
Besides, like many other rivers with populations of anadromous fish, the Wenatchee and lower Icicle does not support a big 'trout' population so those rainbow trout you catch are most likely small steelhead. These rivers used to be heavily stocked with trout back in the day but that stopped a while ago. If you want to target trout, head to the Icicle above the hatchery where it is legal to fish for trout (except bulls). There is way better access anyway and it is much more scenic. Like anywhere, if you can cast from the road, you're not going to find much. Bushwack a bit and you might be surprised! Well, maybe only surprised if you have a 3wt, lol. Have fun!