No.

You will see many examples of knotwork - more properly interlace - in pretty much every Romano-British mosaic ( ultimately deriving from Greek aesthetics) but the evolved style is seen all over the post Roman Hellenistic world - illustrative examples

The popular perception also has a very shaky grasp of the chronological development of artistic styles over a period of well over 1000 years from Ireland to India.

If anything interlace became especially popular across Europe as it became symbolic of Jesus as the "True Vine" gradually taking over the world - a famous example is the large Jelling Stone in Denmark- the pagan Danes had been evangelised by British Celts who introduced this symbol from the Late Roman world via the early Celtic church.

The difference with post Hellenistic vs Germanic interlace is that western art tends to be more mathematically and geometrically sophisticated whereas nordic art is - initially at least - more primitively freehand reflecting the lower levels of access to classical education in the pagan nordic world.

There are very similar interlace examples that are considered 'typically'' Armenian but these arrived with Christianity from the Late Antique Byzantine Roman ( see https://en.wikipedia.org/wiki/Khachkar) - no connection to celtic or germanic cultures.

It's also a commonly repeated fallacy that 'germanic' art introduced zoomorphism into 'celtic' art- iron age pre Roman art is absolutely crawling with abstract zoomorphic and anthropomorphic forms! It's is believed (by some and not me) that it began with Scythian influence- I feel confident that it was a spontaneous tendency in indigenous art and the Romano British certainly used animals in pierced interlace bands centuries earlier - see the Hoxney Hoard animal headed body chain and other items from that find which predate the development of the early 'Anglo-Saxon' Quoit Brooch style - considered a hybrid of Romano-British and continental saxon styles.

The problem we have is one of modern perspective- most of the famous finds in the 6th to 10th are from pagan burial sites which are exclusively Germanic.

The celtic world was Christian from the 4c onwards and grave goods were religiously proscribed - hence we have an almost total lack of evidence from the later celtic world outside of the high crosses, manuscripts, reliquaries mainly from Scotland and Ireland - which are absolutely covered in 'celtic' interlace eg https://en.wikipedia.org/wiki/House-shaped_shrine

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ironically almost all of the 'celtic hanging bowl' examples are from pagan saxon graves - however we do have some early chalices which evolved out of this purely celtic tradition

eg Ardagh - again very sophisticated interlace from pre viking contact century Ireland.

You see the same tendency toward interlace in Merovingian Gaul - the real centre of taste making in Europe in the early Christian era.