The approval of your claim for SSDI was an administrative one. It is not medical evidence. Therefore, it has no bearing on any decision that OWCP makes. If, for some reason, SSA terminates SSDI, you do not need to notify OWCP unless SSDI is converted to a retirement SS benefit. Generally, that only happens when you reach your full retirement age for SS (anywhere from 65 to 67, depending upon when you were born.)
If OWCP does terminate (or even reduce its benefits), do notify SSA. Your SSDI benefit probably is subject to the workers' comp offset. Ergo, you want to be sure that SSA has the correct info and makes any appropriate adjustment to your SSDI benefits.
A second opinion physician is supposed to base his opinion on the medical info that OWCP furnishes and his/her physical examination of you. You can inform such a physician about the status of your SSDI claim, but that decision really is not medical evidence. Therefore, it really should not matter one way or the other to the examining physician.
In short, each program has its own rules and regulations and relies upon the info that it receives, not the determination of eligibility made by some other Gov't program.