Yes, they did. The practice is described in the sagas, not least the story of Domalde, a legendary Swedish king whose reign was plagued by bad harvests and starvation, leading to the sacrifice of oxen at the blót at Uppsala, then men, then ultimately the king himself before prosperity returned. The Poetic Edda also describes sacrifices of thralls at funerals of important people.

The 10th-century chronicler Ibn Fadlan gave a well-known eyewitness account of human sacrifices in connection with Volga Viking funeral. The German bishops Thietmar of Merseburg and Adam of Bremen gave secondary accounts that were almost contemporary (written at the tail end of the Viking age).

Most importantly though, there's archaeological evidence of what would appear to be thralls following their masters into death. For instance, the grave of the 'elk man' at Birka. It's the grave of an older man, buried with a spear, shield and arrows and an elk antler next to him. Next to and partly on top of him was the skeleton of a decapitated younger man in a contorted position with his head next to him and no personal effects. This grave is dated to the late Vendel period, not the Viking Age though.

Another grave in Bollstanäs in Sweden had two decapitated men, belly-down, on top of a layer of burnt material, with the remains of a third man and animals, and objects. The interpretation being that they were thralls who were executed and placed on the funeral pyre of their owner.

I haven't seen the TV show so I can't really comment on it. But very little is known about how religion in Viking Age Scandinavia was actually practiced.

The common picture of there being a monolithic, homogeneous religion and culture across Scandinavia is very oversimplified, not least when you look at the archaeological evidence (e.g. Svanberg, Decolonizing the Viking Age. 2, Death rituals in south-east Scandinavia AD 800–1000, Anders Andrén's Roads to Midgard) which points to quite disparate customs just in the limited area of south Sweden/east Denmark, but also differences between social classes. To an extent, a lot of what people think of as 'Norse mythology' may have been mainly an affair for the upper classes. (not to mention written down centuries later and filtered through an Icelandic Christian author; Snorre). There's so much written about mythology based on the Eddas, cross-referenced wiki articles on all the gods and so on, that it's very easy to miss the forest for the trees and get the idea a lot more is known than is actually the case.

Sources on the the archeology here is Fornvännen, so they're pdfs in Swedish with only a short English summary: On the 'elk man', on Bollstanäs.