My son's BF was drafted as a senior with no eligibility in the third round, 200K I think he got?
Yes he will get a lot more chances than others just because of the money he received and his draft slot.
CD brings up an important point, you must have your at bats or innings to improve, and the lower you are drafted the greater chance there is of not playing everyday. IMO, unless you do get lots of money, which means more opportunity, get your work in where you will get more playing time, which for most is in college. It might mean less money when drafted, but you have put in the time needed to advance quicker.
Someone told me once that a hitter needs about 3K at bats from age 18 and up to reach the skill level needed to even become a consideration. You will notice that many college hitters will arrive in MLB quicker than others, only because they have put in that time needed to improve their skills. I am not sure this is correct, but makes lots of sense to me.
For pitchers there are other considerations, mainly the wear and tear on the arm.