After watching it again its difficult to answer.
On the one hand quaid dreams about the brunette lass before he goes to rekall, which might imply these are his memories before the memory cap was discovered by Rekall, who in the process remove it and this releases his agent persona.
On the other hand, you only ever see quaid after the point he is drugged, so is the memory cap just part of the agent program, and it also is using his dreams as a basis for her character.
I like to think its the first from the look on sharon stones face at the start when he mentions he wants to go to mars. She is concerned and does her best to make sure he doesnt go.
Also the guy at his work seems to have the same agenda.
Suppose this is no defintive answer.