This is an intriguing idea.
What was the expected / actual British level of troops in NI at this time? And how quickly could they have been reinforced from England?
It feels the Irish forces are far too small to do anything useful, beyond the initial surprise. And even then I’m not sure how much of a surprise it could have been given how porous the border was.
Even the Irish Army's general staff concluded that it would be a disaster. The original intention had been intervention against the rampages of the B Specials when the rioting had reached a peak in mid August 1969. By the time the planning had been sought and delivered, the British Army had been deployed onto the streets of NI. There were 3 resident regular battalions at the outset and that more than doubled with deployments from the UK by the end of August. They could have been reinforced very quickly from the UK and if need be Germany. That's of course not counting the paramilitary security forces in NI. The RUC and the B Specials.
Ironically, at leat one of the objectives of the mooted commando raids, the BBC studios in Belfast, had British troops deployed as a result of the rioting, so any attempt to storm them would not have been without active resistance.
Overall the idea, wooly headed as it was, was a quick intervention, maybe 48 to 72 hours allowing for Catholic/ Republicans in the North to escape their Loyalist tormentors and to call for UN intervention. I'm not sure how members of the Irish cabinet reconciled the idea of UN intervention and presumably the deployment of blue helmets on the streets of Derry and Belfast with:
a) The fact that under international law they would be the aggressor.
b) The tiny but somewhat inconvenient fact that Britain sits on the Security Council, with veto powers, of said United Nations.
c) The fact that Britain was a founding member of NATO, with all that goes with that.
None the less, the plan was roll over the border, declare victory and bugger off again.
The Mouse That Roared seems to have been the basis for the concept of operations.
Surprise for the British Army/ Government? The old military maxim: 'the object of a successful operation is to
surprise the enemy not
astound him' comes into play here although, in this instance, it probably would have played to the advantage of the Irish Army, at least initially. Nobody in their right mind would have expected the Irish Army to roll over the border.
The deployment of large portions of the Irish Army was noted, it coud hardly be otherwise as it absorbed a sizeable portion of Ireland's public transport fleet , it was publicly announced and as you point out, the border is porous. Remember that the establishment of field hospitals and deployment of troops along the border actually took place. Then there was Lynch's speech which did cause quite a bit of alarm in Stormont and Whitehall.
That said, if the cover for the deployment is the establishment of field hospitals in the guise of humanitarian relief and given the physical proximity of the identified military objectives (lodgement in/ around Derry and Newry) then no doubt some level of tactical surprise could have been achieved. Both Derry and Newry are what? About a five to ten minute drive from the border?
Newry, ironically, is the more likely surprise. Newry had and still has an overwhelmingly Catholic population and had not suffered from the sectarian violence taking place in Belfast and Derry. It also had a Cathloic majority council. Quite a pointless objective really but the Irish Army was attempting to be realistic about what it could achieve in a military and logistical sense and had concluded it wasn't much.
So, given that the planning objectives were to hit RUC stations, no doubt there would have been initial firefights with the police. Sidenote: The RUC still had Shorland armoured cars in 1969 (shout out to Minifigs who make one in 28mm), so you potentially have more toys to play with.
What would Ireland have done in the face of the swift and inevitable order to cease and desist from the British Government? Well, that's examined fairly well in the RTE doco at the start of this thread and for gaming purposes, having the Irish government decide it couldn't afford to lose face domestically works nicely for a game or mini campaign.