Okay, before we get into this: Yes, I understand that all the Open Game Content is located at http://paizo.com/prd/ and any player with internet access isn't actually limited to the core rulebook. But for the sake of argument, let's say that the player in question has no internet access (they live in farm country in Montana) and only access to the printed material.
If a player is restricted to the Core Rulebook content only, can he create a character comparable in effectiveness and power level to characters using other official source material? Can the player join a Pathfinder Society table and contribute, game mechanics wise, to the power level of the team?
WIll it be as powerful, no.
Can it be powerful yes.
Ofcourse someone with 100 times more otpions and variables will have th eability to make something better.
But a sorcerer just using core is definately very powerfull.
Make a sorcerer that uses arcane bloodline using metamagic on spells that save or die is very powerful. Gets feats like spell focus to make them harder to avoid.
You will definately be a great addition to any group.
Society games are limited in scope; a good society build should start to hit its stride no later than 3rd level, and remain reasonably powerful through 9th or so. With those parameters, yes, you can be perfectly viable using on the Core rulebook...though bear in mind that Society play requires/allows for 3 traits, only one of which can be a Society trait, and the Core rulebook contains no traits whatsoever, so you're going to have to reference an outside book at some point.
The bread and butter of every Wizard I've seen lies in the Core rulebook spells; the stuff in Ultimate Magic and other expansions is largely situational and/or utilitarian. Martials do fine as well using Core feats, though I suspect Monks will miss the Style feats from Ultimate Combat the most. I'm not a huge fan of any of the Sub-Domains for Clerics, so again you should be fine using the Core rulebook.
Some classes get major boosts from the splatbooks. Barbarian is probably the biggest winner, but monk does OK too (still fairly weak in most cases, though). The others don't change a huge amount, except for certain OP spells.