Splitboard Avi Response

A skilled backcountry rider is a skilled backcountry rider. 

There are so many variables that go into a partner's ability to rescue someone caught in a slide.  Issues such as keeping one's head, the ability to quickly locate a buried victim, the ability to shovel through avy debris, the rescuer's ability to ski, ride or boot pack through or around avy debris or possibly how quickly they can skin back uphill for an uphill victim.  A group's ability to organize itself efficiently into tasks and get everyone's beacons switched to search is also significant. 

On top of a partner's skill and group dynamics, there are so many possible scenarios of how a slide happened and how a person needs to be rescued.  Most of which would have no time penalty between skis and snowboard.  If a scenario did have a time penalty because of a transition back to tour mode, any lost time would be minimal for a skilled splitboarder who transitions quickly.  I transition as quickly as many skiers.  

If there is any difference between being on skis verses being on a snowboard it is minimal and probably completely irrelevant when all the other factors are accounted for. 

Excellent question.
Important because when the shit hits the fan, you'll do what you've planned for. No plan? who knows what you'll do.

My view is:
Either boot or ride down to the search area but critically, if you boot, don't leave the board behind. Always take it with you.
Either do the downward grid-search on board or boot.

If the grid then needs to go uphill/ sidewaysand the terrain won't support booting: Inform the leader that you need to transition to skis, suggest you get put on the outside, or somewhere less critical, transition fast & catch up.

My 2 cents.