Is Turn and slip indicator a good back-up for the attitude indicator?
Is it true that a Turn and slip indicator is a valid back-up for the attitude indicator?


Partially, but it would need to be used in conjunction with one or more other instruments if the Artificial Horizon is inoperable.


Change in the DI and/or compass will indicate a turn.
Change in altitude on an altimeter will indicate a climb or descent. Usefulness of the VSI is limited in this sense. 



  To what extent is a turn and slip indicator a back-up for the attitude indicator?


With every one of the instruments on an aircraft there are backups. Sometimes this may be an entire second stack (eg Radio may have a complete second system, AoA sensors may be duplicated) other times you need to use a combination of more than one other instrument. In the case of a Turn/Slip indicator the latter is true. You  use a combination of DI, VSI, altimeter as described above to get a picture of your attitude when the Attitude Indicator itself is inoperable