As you ask, I am leaving aside the moral implications. Regarding the practicalities of getting away with it:
1. When you buy a house, the transfer deed must be stamped; to do this, your solicitor must submit your PPS number to Revenue.
2. How well integrated are Revenue and Social Welfare right now? Not the right question. (answer: not very well, unless of course your name is Dolores McNamara, if some of the Sunday papers are to be believed)
3. The right question is "will Revenue and S.W. become more integrated, and when they do will they have data on file which lands me in deep doo doo?"
To this there is only one possible answer;
If you are a poor person, and likely destined always to remain so, there is some perverse logic to engaging in S.W. fraud. But if you ultimately intend to be a successful and affluent man of business, I think it is very foolish indeed to contemplate this action. Ditto, by the way for your "off the book" income.
It may be possible to organise your affairs so as to have your startup company but to (perfectly legitimately) continue for a while to have a small income which does not disqualify you from S.W. payments. As I understand it, once you go over a certain income, you stop receiving the lone parent allowance. There is nothing inherently wrong in you drawing a very small income from a company which is in a start-up phase. There might also be an asset test, but it is possible that your start-up company has very little value as an asset just yet. There may be other options. I think you need to have a good think about your attitude to fraud - and in saying this I am quite deliberately leaving aside the moral issue - in terms of the risks versus the rewards.