I'm going to assume your existing detectors are wired to interconnect and not just for power. In this case, you'd basically have two sets that don't interact with one another. The Nests only interconnect over wifi, not the wires. If you get the wired Nests, they're two wire, instead of three, and it's just for power.
If you don't mind the lack of interconnection between systems, go for it. They won't interfere, but won't work together either. One of the things I really like about the nests is the fact that they're connected, and anyone in the house will know about it if there's a fire or CO buildup.