Yes, most food processors will be able to liquefy peeled fruits. That said, a juicer is the superior tool for turning fruits into juice. The key difference between these devices is that a juicer will separate out the extraneous, non-liquid components of the fruit whereas a food processor will smash them all into one mixture.
The resulting puree from the food processor will essentially be a sludge and likely not particularly homogeneous. Some fruits will be drinkable in this fashion, but others will be more like a paste. The juice from a juicer will be comparatively less viscous and often less bitter.
Food processors are awesome tools for chopping, grating, slicing, and shredding. They are not particularly good at producing drinkable juice from most fruit. If given a food processor and a fruit and tasked with making juice, I would reach for a reamer or even a fork before I throw it in the processor.