Optimize queries from MySQL SP/Triggers/Functions
You have actually asked two questions:


"If a query is written in MySQL SP/Triggers/Functions/Events is slow, it will not be logged into slow log file"

Answer: it will not be logged in standard MySQL server. Do take a look at the Percona Server extension for the slow log: in particular look at the log_slow_sp_statements configuration variable. It does what you want: the slow queries within routines are logged. Note that this does not apply to triggers.
"Do we need to optimize each SP/Triggers/Functions/Events individually?"

Answer: well, of course. Each and every query needs to be as optimized as you can, depending on your requirements. A routine is not a "magic solution" that causes inner queries to run faster...