Picking up opportunity card on exiting career path
It would, if you actually landed on the Opportunity Knocks square, which only happens 1/6 of the time. When exiting the career path, you continue moving clockwise the full number of spaces that you rolled. Additionally, you need to meet one of the requirements of the new career to enter the career path that the Opportunity card sent you to. From the rule book (2003), (the 1990 version has the same rules, but they are not written as clearly).

Move Your Pawn - Moving After Rolling: If your pawn is on the main path, move it clockwise by the full count of both dice. If it's on a Career Path, move it toward the end of the path by the full count of one die. (page 3)
Before entering the career path, you must meet one of the requirements Listed on the Entrance space (unless you played the Special Opportunity card, which let's you in for free). For example ... (page 5)
Completing A Career: When you leave a career path, continue moving clockwise along the Main path. ... (page 5)