Social status is a fine tool if the PCs are generally about the same status. If one is of greater standing than another, however, there can be problems. High status people lose "points" for hanging around with lower-status people (in some societies).
You may want to look at Oriental Adventures and its discussion of castes. Castes are, in essence, rigid social status definitions.
Other considerations:
1) Make sure your players understand what their social status means. If the low-born are not supposed to look up in the presence of the nobility, that applies to the character no matter what his/her level is. A 10th level low-born Fighter is still "dirt" to a 1st level noble Aristocrat, and had best not speak until spoken to, etc. (Lawful societies & characters are more picky about this than Chaotic ones are.)
2) Design your adventures to keep in mind the social status of the characters. Some jobs will be ones they should refuse because they are tasks for those "beneath them". Other tasks might actually help their social standing.
Perhaps, instead of social class, you should consider the Reputation variant from Unearthed Arcana. That still allow the characters to "grow" in the esteem of others without the sometimes-awkward interactions that social classes can bring.