No.
At least, not willy-nilly. The DM should make exceptions when it's cool to do so, and bear in mind the rarity or regularity of his descisions. Maybe there are no elven wizards, because although they live to great age, they display little patience for lengthy and sedate endeavours like research or ruminations? Or maybe humans are never born with sorceror's blood UNLESS they are of mixed ancestry? Or maybe only elves? Those options are already present in Pathfinder, but could be molded as you need for your own campaigns. A Human brought up to be an Elven Blade Singer (D&D 3.5), for example, would be really cool... if it was a really great reason, tied into a compelling back story approved by, or tailored by, the DM.
Or a lizardman whelp that was at first held prisoner by the folk of Amindol, a small human-majority hamlet near a small Shrine of Torm. Eventually, through proving himself (and not being subject to abuse, or at least not on the same levels as the Blackscale lizardfolk tribes would have made him suffer in the Sangrothi Fens, were he captured there), he was taken on as a camp guard, and later purified and ordained a neophyte and squire by the Church of Torm for one of the Templar there, an older man who saw in the creature the spark of a redeemed soul. Eventually, as the creature matured and arrived at his full size and strength, the aging weapons-master taught the reptile the ways of the Holy Order and, on his death-bed, passed on his blessing for the lizardfolk to take the Test Of Faith, and become Zalak-Thun, the Paladin Lacertilian of Amindol.
I, totally, got off on a tangent.
So, in summation, my answer is still yes.
...
yes.