Answer: This is a difficult question to answer given the various possibilities within your scenario in terms of time sequence.
If the patient is VSA due to a FBAO, then the priority is CPR, consider removal using BLS maneuvers, and if the obstruction cannot be removed, transport the patient to the closest appropriate facility without delay following the first analysis.
Depending upon when the obstruction is relieved, if the patient remains in cardiac arrest, then you are to follow the Medical Cardiac Arrest Directive which states that you are to analyze as soon as possible. As part of the Medical Cardiac Arrest Directive, CPR is initiated first however only until that first analysis can be performed. There is not a specified 2min block of CPR to the initial analysis.
If the obstruction is relieved following the first analysis under the FBAO Directive and prior to the transport, then again, you are to follow the Medical Cardiac Arrest Directive.
If you are wondering if for some reason what to do if the obstruction is relieved immediately during or immediately after that one initial analysis, then logic would suggest that in that rare case, there is little value of having immediate successive analyses and we would suggest continuing with the 2min of CPR cycle in this rare situation only.
As for the Medical TOR, if EMS did not witness the patient arrest (which would be somewhat odd to then be certain that the patient was initially a FBAO induced arrest), the obstruction was then relieved allowing the full Medical Cardiac Arrest Directive to be completed with no shocks delivered and with no ROSC, then yes, in this situation TOR could be considered and a patch to BHP would be required.