Sycophantic is obviously a word, because we understand what it means.
Furthermore, it obviously hasn't been a word since at least 1800:
https://books.google.com/ngrams/graph?year_start=1800&year_e...
GOP wrote syncophantic, with an n. Which is not a word. Well, not a known word at least.
On the other hand https://books.google.com/ngrams/graph?content=syncophantic&y...