Say an event happens then renders the Ard-Righ seat vacant and either there is no one alive to succeed him or/and no one wishes to fight for the seat or is strong enough to take it. Would it be possible that for a period of time for the high-kingship to be left vacant?
Before Brian Boraime the high-kingship was moreso an honorary title based on tradition and geneaology. It alternated between the various Uí Néill dynasties but the high-king possessed very little power in terms of subordinating other kings.
Brian took the high-kingship in 1002 and spent the following years consolidating his power, even subordinating some Scottish kings. The Book of Armagh refers to him as "Imperator Scottorum" or "King of the Scots". The Earl of Mar in northeastern Scotland is noted in the annals to have died alongside Brian at the Battle of Clontarf in 1014.
Brian's death in his hour of victory at Clontarf created a vaccuum for the high-kingship, which altered the course of Irish history forever. The break from the tradition of the Uí Néill high-kings before Brian meant that he who had the greatest military might could be high-king.
The following two centuries shows various kings vying for the high-kingship. Due to the fractures dynastic nature of kingship in Ireland and the ambition of various kings, none achieved the true high-kingship that Brian had, and are reffered to in the annals "rígh Érenn co fressabra" or "high-king with opposition". To qualify for this title the king would have to have either the Leth Cuinn or Leth Moga as their subordinate, and a small area in the other half of the country.
Your question is somewhat speculative, but I don't think it would have been possible to have a vacancy due to the fact that there were too many ambitious kings vying for that position at once.
Sources:
Donncha Ó Corráin, 'Ireland before the Normans'.
Sean Duffy, 'Brian Boru and the Battle of Clontarf'.
F.J. Byrne, 'Irish Kings and High-Kings'.