If it is possible at all, Onshape is probably the CAD tool to use. Many people can work on the same project (or even the same part) simultaneously. Unless you want to fork over $1500 a year for a pro account, all free account projects are publicly viewable (and in the public domain, last I read the fine print).
Accuracy and what to do when the plans are not clear is a problem. You have to model something, and then that guess becomes gospel. What about purchased parts or parts made from templates that are not fully dimensioned?
As a side note, as a mechanical engineer, I'm frustrated by the format of the aircraft plans that I've studied so far. Show me a fully dimensioned drawing of the finished part! It's like the difference between step-by-step driving instructions and a map showing where the destination is located. The directions will get you there, but you won't know where you are.