You are correct that a network model would be better than a set of standalone models to see the true effect – as you say they interaction between junctions is as important as whether the junctions themselves are within capacity. The technical data on the junction models would include queue lengths that would allow you to get a feel for whether this is an issue if you measure the links between the junctions (Google Earth). The flipside of that is that network models are often better at dynamically assigning demand and balancing the demand over the road network.
If this is an allocated site included in local planning documents then the local authority are likely to support it. And if the planning document has been adopted as local policy then that means the authority will back the sites in that document so long as they are developed within the bounds of other policy.
Large developments will inevitably increase local traffic and creating additional road space is not always a good move as there are always pinch points in the network; so in effect an improvement somewhere often just moves the problem on.
What I would be looking at in detail is the measures the development will be putting in place to encourage sustainable transport. For 2,000 units these should be pretty significant and be a realistic alternative for employment and school travel both to the development and the wider community. For instance do the measures put forward look reasonable to generate 35% of people walking to work/school. Pushing for increases to these is more likely to gain council backing than opposing the whole site if it has wider policy backing. As mikewsmith says diving too deep into the modelling detail is often unrewarding.