Since you only want to see if the user exists, you don’t want to query the entire object. Only query the id, it exists if the scalar return is not None.
exists = db.session.query(User.id).filter_by(name="davidism").first() is not None
SELECT user.id AS user_id
FROM user
WHERE user.name = ?
If you know name (or whatever field you’re querying) is unique, you can use scalar instead of first.
The second query you showed also works fine, Flask-SQLAlchemy does nothing to prevent any type of query that SQLAlchemy can make. This returns False or True instead of None or an id like above, but it is slightly more expensive because it uses a subquery.
exists = db.session.query(db.exists().where(User.name == 'davidism')).scalar()
SELECT EXISTS (SELECT *
FROM user
WHERE user.name = ?) AS anon_1