Can you lose SR in placements?

This is not an accurate representation of how it works.

Players’ 10 placement matches will start with Blizzard’s best estimate of each player’s MMR for matchmaking purposes15. A player’s initial SR will generally be close to his previous season ending SR, with a relatively ordinary adjustment based on 10 placement matches.

There’s of course more detail about border cases in the article. See the “Season Transitions” section.