Heck no! They were awesome!
That says what I believe. I didn't find them the least bit scary, really I found them to be a massive upgrade of the TP Tears of Light, and THOSE weren't scary. The music wasn't really forboding to me as it was "watch your back" [to me, foreboding means something terrifying is drawing near, whereas "watch your back" just means stay alert].
blackice_cc actually brings something up – the Guardian Chase music actually reminded me of the Resident Evil series. And while I realize the "scare" in both series are of completely different nature, Skyward Sword somehow seemed to try to reach over into RE and grab some of that feel, what with the bizarre enemies, searchlights as well as 'assertive' music.
So no, I don't think the Silent Realms were scary, but DEFINITELY fun.