Having had dual coverage for a while, I can say that, at least in my case, there was no significant increase in coverage offered by having two policies, but a significant increase in paperwork hassles.
The minute you check the "yes" box beside the question Is this patient covered under another policy?, you must identify which policy is the Primary and which the secondary. And you don't get to decide.

At the time this happened to me, this was determined by the birthdates of the policy holders. First Birthdate of the calendar year is primary, so my wife's August birthday made her the Primary to my September.

Now, Doctors and Hospitals will handle the paperwork these days, but it may take an extended period of time to finally put the bills to bed.

I currently have dual coverage, Primary from my employer's BCBS PPO plan and Secondary through a military retirement. The secondary has paid NOTHING in the last 18 years since I retired. If it were my primary, it would be similar to a POC 80, but as a secondary it is pretty useless. Fortunately, there's no out of pocket cost for this "coverage" (Twenty one years in Nuclear Submarines was enough payment).

Will his new company insure him without exclusions for pre-existing conditions?

Most health and life insurance questionaires have the ubiquitous "Have you been diagnosed with or treated for?" questions which disqualify you for coverage of certain conditions.
As in Brian's case, it a tough choice to give up coverage you have in place, knowing that you might not be able to obtain coverage.
I hope I haven't muddied the waters here. Just trying to share my experience.

Good Health,

Chuck