The only way the South is going to invade the North would be in the event of a unilateral withdrawal by the British government or the complete collapse of the government in London to internal revolution or foreign war.
So... not likely.
Not perhaps as unlikely as it seems.
Both the Conservative and Labour parties in the UK had contact with the IRA. The failure of Sunningdale along with the election and re-election of a Labour Government in February and October 1974 made the possibility of a British withdrawal from Ulster very real. Harold Wilson was interested in pulling out and making Ulster an independent Dominion - I suspect that would have led to civil war.
Dublin knew nothing of any of this and were appalled when it came out years later. Wilson resigned in 1976 and James Callaghan, his successor, was opposed to any British withdrawal from Ulster but if we suppose that Wilson announced in mid 1975 that, in exchange for a ceasefire with the IRA and the latter's agreement not to pursue any further terrorist action on the UK mainland, all British troops would withdraw from Ulster by October 31st 1975 and that the following day Ulster would become an independent Dominion within the British Commonwealth.
I simply can't see this ending well - it's basically what was seen in many post-colonial rapid withdrawals from India to Angola. Whether the differences are ideological or religious, the removal of the colonial power simply allows unresolved grievances to re-surface. Ulster would have fallen into the abyss of internecine strife and it would have been equally intolerable for both Dublin and London.