Depending on your meaning of success, I believe it can be yes in two different ways. Due to the fact that teams generally do not like to give up on early round picks, they usually hang around longer than guys who were picked in the later rounds. Therefore due to their drafted position and the length for which they are on their teams, they make a lot more money and therefore would be more successful than guys drafted later.
It should also be yes statistically as well, based off of the high competition in college it's easier to project what a player would be able to do at the next level. Also with technology today, scouts also have access to all of the players games and can watch a player for what he is good and bad at. While in the draft all of the players are very talented the best players for the most part have been taken in the earlier rounds.
I would not say all first round picks have successful careers as some may have burned out in college and can not keep up with everyone being as talented if not more talented than they are. Elite players are the hardest ones to find. A draft usually will only have 2-5 elite guys that will simply tear up competition at the next level no matter who they go up against. For example, there has not been an elite QB drafted since Andrew Luck in the 2012 draft. Before that, Aaron Rodgers in 2005.