Look, I am as much a "apologist" for the fighting qualities of most units, including the 11th Corps. However, the fact of the matter is that a core of the 11th was derived from "Blenker's" division which, unfortunately, was a very flawed combat unit. To begin, it contained two vasty divergent officer materials; one, cast offs from the revolutions of 1848, intellectuals and free spirits, the other (and sometimes these overlapped) professional German soldiers, soldiers of fortune, etc., who never quite grasp the volunteer soldiering of America.
Most importantly was its service record. Blenker's Division was sent to Fremont's mountain command and proceeded after detraining without even a map. It blithered into a snowstorm before being found by Rosencrans who described them as a sorry lot of soldiers who had eaten all their dogs and most of their horses.
This set the tale. In the valley Blenker's men were notorious for plunder - even among the Federals - and were very undisciplined on the march. Tactically, their most famous and well drilled unit, the 8th New York, was destroyed in a single volley for failing to send out skirmishers. Their other regiments were defeated at Cross Key's by two demi brigades of Confederates (not a very good showing) who attacked them and drove them back over a mile.
At Second Bull Run, some of the men, now Sigel's Corps, fought well and fought ably, but still other's had the indiscipline stigma (earned or unearned).
I think it very plain that, even if you are a unit that starts as an exceptionally strong combat unit, well-disciplined and adapted in the art of war, if you are allowed a period, as were Blenker's men, starting in the snowstorms of WV, to get that little taste of, what I would call barbary military service, it is very difficult to take the stink of that indiscipline off. After all, you have guns, you take what you want and even your officers partake?
Was there something "wrong" with the 11th corps?
It has a mixed bag of combat record; I have approximately 8,500-8,700 casualties of which 3,000 are captured. It has elements at Chancellorsville and Gettysburg that fight magnificently; however, other elements fight, shall we say, poor. When combined with the 12th corps to form the 20th the men have a respectable combat record throughout the war.
My read, the core "Blenker" men started the war with an officer corps made up of a mixture of professors, intellectuals, and pirates, and didn't include enough professional soldiers not looking out for their own skins. Circumstance put them in a position where all discipline broke down. Habit, course of conduct, and leadership indifference allowed this indiscipline to fester in the valley. A series of weak leaders did nothing to fully break this habit (some, like Barlow, may have corrected it if given the time in his division, though besides Von Gilsa his men were mostly blue-blooded Yankees).
The history of the corps in the east is being led by Blenker, Sigel, and Howard. Howard, though being the best of the bunch, did not understand the material he was given to command (immediately canceled the lager beer ration, etc.).
As a result, the 11th corps was neither given a chance to establish some esprit de corps nor able to effectuate a battle honor, properly prided on as its own. The leadership structure and identify suffered by the constant transition, the weak leaders, the buffoons who served early, and the lack of support from the rest of the army (used by Hooker as a Chancellorsville scapegoat).
When molded into the 20th corps with 12 army leadership the men fought as well as any in the Chattanooga and Atlanta campaign and fought well across the Carolinas.
Just shows a huge lesson on leadership and culture. Also, you cannot ever let the mask of discipline slip or you end up with an armed mob.
So, did the 11th fight well on July 1st? With a few notable exceptions, NO.