No. In that case too you won’t get the Pay Protection. The reason is the same. Even in the case of leaving a Govt. sponsored school (through WBRSSC) and joining a Govt. sponsored college (through CSC) won’t fetch you the same.
Only, if you were posted in a Govt. school (through PSC) and were to join a Govt. college (through PSC), you would have been entitled to get pay protection.