Not necessarily.
1) DNA doesn't get preserved in fossils. Fossilised remains are, by definition, not the original tissue but rather a mineralised mould of it.
2) While we've found huge amounts of fossilised remains of animals and plants covering just about the entire process of the evolution of life, the fossil record is far from complete in the sense that we can find every individual or even every species over the last 3 1/2 billion years. Not every animal that dies leaves a fossil behind - and even if it did, we'd have to dig up the entire world to find it.
3) In order to leave recognisable fossils behind, Life 2.0 would have to be successful enough to evolve at least multi-cellular forms of life. If it comes along at a point where Life 1.0 already dominates the entire biosphere, it might not survive long enough. That's one of the reasons why people looking for "alternative" forms of life in the few areas that don't seem to support normal life - say, arsenic-heavy environments, isolated underground lakes, and goth gangs. So far they haven't found anything conclusive.
That's not to say it has or hasn't happened, but that if it did happen, it's far from certain that we'd be able to find proof of it.