If the name plate details shows the current drawn by a particular 3 phase motor is 30 ampere, is that mean the ammeters connected to each phases will show 30 ampere reading?

Yes....although the readings may not be exactly 30.

If motor is Delta connected; yes, all three meters will show current may not be exactly 30 amps. If motor is Star connected the current would be 30 / 1.732 nearly shown by all three meters.