Not exactly.I feel that allot means more about give by a body or person authoritatively while allocate means more about give according to certain rules or through certain procedures, but allocate is used more often.
The basic idea of 'allot' is to share something out (divide it) among a number of people.
'The charity allotted funds to a number of deserving cases.'
The basic idea of 'allocate' is to put something in its proper place.
'The manager allocated a different task to each member of the team.'