Er...no. It's not a 'must' for check & training positions. The C&T system exists outside the instructor rating system. Check &/or training is an approval unrelated to holding (or have held) an instructor rating except that in recent times passing some form of teaching theory has been required. An instructor rating is (or was) accepted as an equivalent.
However, the above doesn't say that an instructing history wouldn't be useful, or even preferred/specified by any particular company, just that it's not mandated by CASA**.
**unless things have changed in the last few years.