Doubt it; Florence Nightingale was training nurses at this point and they'd caused the death rate in Crimean hospitals to go through the floor, and germ theory did exist (it just wasn't - yet - dominant). Meanwhile the sanitation movement had begun decades ago (1830s and 1840s) in Britain.
Revolutions in ideas sometimes don't come all in one go; they trickle in over time.
I don't actually think they did. You can't really ascribe all deaths in hospitals to the actions of surgeons, and the numbers that I've looked at thus far have been deaths recorded in hospitals so may exclude anyone who didn't make it to a hospital (like all the battlefield burials).
For example in the Atlantic region in September and October 1862 there are 1,130 gunshot deaths listed (of which 702 are in September), but the Maryland Campaign alone (disregarding the Northern Virginia campaign) saw over 2,700 Union dead in the battles - and of those most would not have made it to hospital in the first place, while those who died in hospital would be down as "wounded" on the reports, or perhaps "mortally wounded".
The figures I've used above represent a minimal number of Union dead by violence, and are certainly lower than the true value.
The statement about germs being the source of infection is literally true. The medical people of the 1860's were ignorant, not stupid. When Mother Bickerdyke & other female nurses were in charge of a hospital, the survival rate went up. Their secret weapon was soap. They also boiled soiled linens. In Memphis, she ran a hospital, laundry, chicken farm, & vegetable gardens that supported wounded & recovering soldiers. Sanitation, wholesome food & compassionate care had a dramatic effect.
Directly related to the discovery of germs was the absencence of silk for sutures in the Confederacy. The substitute was horse hair, which the Roman's used. Cotton thread acted like a wick & drew infections into a wound. Doctors noticed that with hair sutures, there was dramatically less inflimation than with silk. The reason was that stiff horse hair had to be boiled to soften it. Empirically, it was obvious that something had happened, but no body knew why. In the chain of events that led to the discovery of germs & how to prevent infection, horse hair sutures was a first stepping stones along the path. Louis Pasteur made his initial discoveries in 1863-64. From that point to the end of the 19th Century, Lister & others introduced the anticeptic principle into surgery. It was not until 1877 that the link between insects & diseased transmission was discovered.
It it almost inconceivable to a person alive at this time of pandemic in 2020, but until the empirical evidence of the efficacy of Mrs Bickerdyke's lye soap, the efficacy of basic sanitation was not recognized. One of the most powerful antiseptic things you can do is just was your hands. Izabell is in 4th grade, she can tell you al about it. In the 1970's when I was Peace Corps Volunteer in the Andes Mountains, teaching simple hygiene to Indian midwives was one of our programs. Amoebic dysentery was endemic. Just wasting your hands is essential to avoid ingesting the amoebas. 100 years later & we were fighting just like Mother Bickerdyke.
At Stones River NB we do Sanitary Commission living history programs. The history of the advances in medicine is a big part of that story. Here in Murfreesboro, we have the whole history of the war, not just 3 days of mass murder to represent. It is a living historian's delight.