No. But Twin Peaks was nonetheless a “first” in significant ways; and a number of commonalities in many more recent TV series can be traced back to it.

The original Twin Peaks series aired during 1990-1991. But Hill Street Blues, a TV series that aired from 1981 to 1987, also had storylines that continued from one episode to another. Going back further, Doctor Who, beginning in 1963, had stories that spanned multiple episodes.

Before that, we find little in the way of major TV series for adults with continuing storylines; but there were any number of children’s series that did. These were typically in the form of “serials”: melodramatic adventure stories broken up into a number of segments, all but the last ending in a cliffhanger. Before TV became popular, many children’s serials were broadcast over the radio in weekly segments, or shown in U.S. movie theaters on Saturday mornings. When TV viewing by children became common in the 1950s, it was natural to move the serial format over to TV. Since a serial segment was typically shorter than the time slot of a TV show, a segment might be included as part of a longer variety show. For example, early seasons of The Mickey Mouse Club, which first aired on TV in 1955, included a serial segment, roughly 10 minutes long, in each episode.

However, Twin Peaks did represent a break with the above traditions. The various children’s series, along with the early seasons of Dr. Who, would have a single story that lasted perhaps 5-10 episodes, and then the story would end, and a new, completely separate story would begin. In Hill Street Blues, each episode would weave together multiple storylines, some of which might end within a single episode, while others would be continued in later episodes. In contrast to all of these, Twin Peaks focused on a single storyline that continued for an entire season. And it was a prime-time TV series aimed at the mainstream adult market (as opposed to the more niche market of a show like Dr. Who, or the various soap operas). Shows in this format soon became commonplace; but in 1990, it was unique.

More generally, Twin Peaks is credited with demonstrating that a successful prime-time TV series could incorporate elements previously restricted to longer movies. This was seen not only in the continuing storyline, but also in things like lighting and camera work, and the role of the directors in the production. As a result, prime-time television became more cinematic in character.

Serialised television drama started on 12th July 1938 with the first live broadcast of Ann and Harold on the BBC Television Service. It ran for five episodes and told the love story of a society couple. While this had aired in radio form the year before, in August 1938 the BBC Television Service began broadcasting Telecrime. Though this was a TV series rather than a serial, it is notable for being probably the first fiction written especially for television without being a one-off play, and it shows us that the basic building blocks were there very early on. It is the mix between series and serial elements that make most modern television dramas work.

While daytime soap operas were popular on US television from the 1950s, Hill Street Blues in 1981 was the first US primetime drama series to borrow the British ideology of serialisation. It is the first to have arcs between episodes, the first to have multiple plotlines in each episode, and the first to have season arcs - even arcs between seasons. It's considered the first "modern" drama, and its model has become increasingly prevalent in US television.

With Twin Peaks, it was the content that was innovative rather than the structure, and its initial success spawned more horror-surrealist drama series such as Picket Fences and Eerie, Indiana.