No, Anglo-Saxon (or more correct Old English) is not a north-germanic language. Germanic languages per se are traditionally split into three branches: west- east- and north-germanic. English, as do German, belongs to the west-germanic branch. Though it is true that English for a time was heavily influenced by Old Norse (which as a precursor to the modern scandinavian languages sits on the north-germanic branch).
A couple of linguists (one Norwegian) do argue that Old English/Anglo-Saxon died out in the wake of the Danish invasions, and that Middle English (and hence modern English) descends directly from Old Norse (with a large amount of vocabulary borrowed from Old English): https://www.apollon.uio.no/english/articles/2012/4-english-s...
I think you are misunderstanding what Poul Anderson was doing there. He was proposing that without the Normans, English would have drawn on the German lexicon. As the link in the sister comment argues, Old Norse had replaced German as an influence well before the 11th century. So Anderson's construction of hypothetical English vocabulary should have been based on Norse, not German.
>He was proposing that without the Normans, English would have drawn on the German lexicon.
That's not what's going on here, he's limiting the vocabulary to existing English words which derive from Old English and inventing some new words using existing morphemes of Old English origin.
(if you're going to look outside English btw the nearest neighbor languages are Frisian and more distantly Dutch)
