It appears to be valid SQL either way though
Yes, 'now' is valid SQL. It is a String. Therefore you are actually storing the text "now" in that field.
SQLite doesn't care what data you put in what field. See here : http://www.sqlite.org/datatype3.html
Note that it doesn't mention date/datetime/time on that page.
It does of course make it difficult to know what you are retrieving from the database, unless you already have an idea what kind of data is there :-)