Yes and...no. While it's true that within the Imperium alone there is somewhere around million worlds, some even being quite close to modern living standards, the biggest problem for the small man in this setting is that the society, and not just the society of humans, is extremely static. Within Imperium of Man, you're basically doomed by your birth to this position or another. There is no way to really rise in the hierarchy if you're born to anything else than nobility or as a child of some special agent of Imperium, like inquisitors or ecclesiarchs. The absolute best that the normal man can hope for is to become an officer in the Imperial guard, join the Sisters of Battle(if woman) or attempt to join the Space Marines(if born on the right planet, and only if you survive their initiations, which are extremely deadly). It's needless to say that all of these options are such that only very tiny percentage make them.
And it's almost the same for all xenos races in the setting. Some are completely dictatorial to a degree that puts even the Imperium at shame(Dark Eldars, Chaos, Nids and Necrons), while others are merely quasi-dictatorial like the Tau or Eldar, and admittedly slightly more humane than the humans of the setting. It could even be said that the CW Eldar have the greatest amount of free will and opportunities in life, provided that they absolutely and totally accept the unchanging theocracy ruled over by the psychic elite of their race.
Just about the only race that really appreciates talent and to some degree free will is, quite paradoxically, the Orks. And this is completely borne from the premise of their very existence as genetically engineered warmachines who are happy only when they are fighting something, a situation which is luckily in ample supply in this universe. But in their ranks it's completely possible to rise from the total bottom of the society to be the most feared warboss in the galaxy, provided that you survive long enough in completely anarchistic society that uses the teeth of it's own members as currency.