Nope. The Anti-Deficiency Act includes an exception for the “safety of human life or the protection of property.” Subsequent opinions of the Attorney General (found in appendices here), opinions of the DOJ Office of Legal Counsel, and guidance of GAO / Comptroller General have clarified what does and does not fall under this exception. In past shutdowns, OMB opinions have considered the following types of things to fall under the exception: military and national security, public safety such as air traffic control, care of patients in hospitals and prisoners in prisons (and wildlife at the national zoo), things necessary to protect federal property and continue the functions of the Treasury, and disaster relief, among other things. Under common sense interpretations, the heat can also be left on at federal buildings.
Don’t let all these exceptions distort the bottom line: if no appropriations bills have been enacted, the vast majority of federal agencies will largely shut down, and sizable portion of the federal civilian workforce will be furloughed. You can see the percentages here.
As always, my recommendation is to go the most recent CRS report on the topic (I used to be a co-author of it.) It has all the citations and links you could ever dream of to lead you to the primary source material you need to keep yourself busy for a whole weekend reading about this stuff.