Does Microsoft Word recognize the nicknames for ‘big numbers’ like zillion, jillion etc?
There are many informal words to describe a non-specific but really large numbers. Word’s dictionary (at least in English) recognizes them as correct spellings.
If you want to be more specific see Real words for really big numbers in Microsoft Word
Word’s thesaurus offers some alternatives to “zillion” though some aren’t really synonyms (million and billion are specific numbers).