I assume, as was the case with Northern Ireland that the UK is not subsiding Scotland and Wales to the extent that a breakup of the UK could result in the economy in these said places crashing.
You may say Scotland has the North Sea gas buy exactly how much of this revenue goes directly into Scotland (potential area of contention between England and Scotland if the split).
Airbus built parts of the A380 in Wales, again as a result of the British government pushing investment and jobs in the more disadvantaged areas of the UK, so there does exist some sort of cohesive economic/social policy that is not so much England-centric as was the case in the days of Thatcher.
Would the economies of these countries be able to survive? Probably, but then these separate states would be responsible for their own development, and as in Ireland’s case where it managed to get money out of the EU (for education and infrastructural development), Wales and Scotland would have to compete with the newer EU countries for grants and money. But this periphery of Europe/ ERDF fund seems to have dried up, and the EU is not throwing money out in the same way anymore. At the moment the UK has the sixth largest economy in the world, which Wales, Scotland and NI are part of.
Investment is another area, they could lower corporate tax as Ireland did, but you also need to factor in the cost of labor, which comparative to Eastern Europe is probably higher.
On Northern Ireland, the majority of people in the south of Ireland don’t want to join with NI. It may be a mistake (at this point at least) for the two parts of Ireland to join so prematurely, that’s if they wanted to join at all. Besides it is highly improbable that the consent of the majority in NI could be got (now or for years to come) to break from the UK, not to mind to go the next step to join Ireland.
But NI is kinda in a strange situation in regards to what it should do next. It is still subsidized by the UK, perhaps to a less a degree than before. It is a quasi- country or territory but has no independent representation in the EU. All money that comes from the EU goes through the books in London and then is passed to NI, as is the case with Wales and Scotland. Since it is part of the UK, it has no real independent (from the NI point of view) input into EU decisions and has to tow the line of what’s best for the UK. It therefore has no real control on what direction it can take and it can itself only push for investment within what is best for the UK as a whole
I do not think it would serve any purpose for the UK to break up, or for the provinces of the UK to become independent. If you look at the basic numbers per capita income in Wales, Scotland, England, and NI is E23K, E 27K, E 27K, E 23K, then it seems that income across all provinces seems consistent, with a higher income in England and Scotland. No doubt that an independent Wales may be able to pull off a Welsh Tiger economy if it was independent, but then it could also find that independence drags it down