Up to certain limits, of course. Beyond a certain length of time, say 40,000 years or so, you have to use other decay cycles, like Uranium.
But, in particular, H. Kitagawa and J. van der Plicht, in their 1998 article in Science on calibrating the Radiocarbon methods discus the accuracy of the method back to 45,000 years, by comparisons of Radiocarbon dates, versus direct annual counts of varves, and tree rings.
Many others have done similar works, in the decades since the first Radiocarbon estimates were made. In fact, in recent years, a fortuitous find of timber buried by a landslide in a fjord which could be dated exactly, and matched with known tree rings allowed the direct dendrochronology to reach beyond 15,000 years for samples from the northern hemisphere.
You will often hear that “They” have disproven, or proven this that and the other thing. I would ask who they were. “They” tested lots of things. “They” don’t have a source for you to read, though, or a date when the study was done, or a name for the guy who did it, or the methodology used to obtain the data. In fact, you can’t even get a look at the data itself. Only the bald assertion that “They” tested it, and all of science turned out to be a vast conspiracy of idiots.