No and Yes
Uplifting, by its very definition, includes the intention to bring a species to sapience. So, one cannot accidentally Uplift a species.
That being said, of course one species can accidentally increase/change the intelligence of another. For instance, dogs are the only non-human species that understand pointing. Does that make them more generally smarter? No, but it shows that we can impact specific intelligence patterns, which means we could also impact general intelligence.
As for how much intelligence can be influenced, well, just look at humans. We didn't evolve in a vacuum. Who's to say other apes or lions or zebras or something didn't accidentally force us into sapience (certainly wasn't intentional on their part)?
You can't skip the several hundred thousand years of natural selection; without gene splicing, everything you're doing is natural selection, even if you're consciously directing the breeding. But, you can make natural selection go in a direction you want it to go.
See, evolution isn't a straight line, "unintelligent" on one side, "sapient" on the other; chimps are not still evolving into humans because they are fully-evolved chimps that are evolving into the chimps of the future. 335
Without particular selective influences, there's no reason to think chimps will ever evolve sapience in the wild, even on an infinite timeline. After all, there's only one sapient species on this planet, and it's not like jellyfish haven't had just as long to develop intelligence as we have.
If we wanted sapient {whatever}, likely the only way to do it (without gene splicing) would be to intentionally breed for intelligence for a few hundred thousand (or million) years. It takes that long because you're only getting changes with every generation, every generation takes several years to mature, and you aren't guaranteed improvements with each generation. Further, humans have one of the longest childhoods relative to our size, and it's thought this is because of our intelligence. As you increase an animal's intelligence, it's likely the childhood of that animal will lengthen as well.
Which means, ultimately, that some crazy billionaire is going to gene-splice an uplifted {whatever} way before you breed one. I've heard we're really only a couple decades of dedicated research away from uplifting primates, it's just that no one wants to step in that moral quagmire. If that's true (even if it's off by a factor of ten), gene splicing will Uplift a species before selective breeding even if your starting point for breeding was 40,000 years ago (about the time dogs started getting domesticated). 335