Not really. Demand is high. Supply is constrained in the short run in terms of the light sweet crude the [also capacity constrained] refiners prefer. Whether the price movement over the last year has anything to do with peak oil will only be apparent if in a year or two significant additional supply has not appeared on the market.
One of the points many peak oil advocates miss is that the most marginal stripper wells get plugged or at least shut in during oil price busts. Other than in some nasty offshore environments there will not be much in the way of abandonments with the price of oil north of $60. This should tell us a lot about what is possible in terms of flat out production and the absolute depletion curves based strictly on reservoir dynamics.
And there a many, many marginal wells out there. And furthermore, there are even more untapped marginal fields. And in spite of the doomers' claims that "all reserves have been found" anyone who has actually ever done exploration work can tell you that the vastness of the earth (and oceans) are such that we're not even close to knowing what's still out there. Granted, some outstanding fields were found when we moved from wildcatting to technology, and so, it may seem like we've found a great percentage of what may be out there. But let me write this - considering the jumbled geology of the Western US, I think that is overly pessimistic. Heck, you send 10 different people to map the same area of FRANCISCAN terraine in California and you get 10 different maps. And yes, there IS oil mixed in with this terraine. Monterey Formation also has oil. Etc. Until I see Vibroseises in peoples' back yards or in farming area in the smaller valleys, I will not utter the nonsense that we've found everything there is to find.