No. If you activated both PlayStation Plus memberships separately for you then your brother then the subscriptions will be concurrent on the system.
You would have had to have activated both cards on the same account for them to add on to one another.
As for the second part of your question. Normally the only time there is complementary time is when Sony runs trial promotions, or sometimes they bundle free time in with systems. If you add a purchased time to an account created with trial time the paid time is tacked on to the trial period. Eg, you sign up with a 30-day trial then 1 day into this you pay for a 3 month card and enter the code. You'll have 4 mos of PSN+ before it terminates.