It's possible, where it is an arts or music course and a portfolio has to be provided, that some bias could occur
With portfolios, it works like this.
Portfolios are submitted and assessed, and the results of the assessment are communicated to candidates, before the Leaving Cert results are known — indeed, before the candidates have sat the Leaving Cert exams. Applicants are placed on a ranked list on the basis of the portfolio assessment. This list is provided to the CAO.
When the exam results come in, the CAO offers places to candidates in descending order from this list, provided their exam results meet the minimum academic entry requirements for the course they have applied for.
The result is that there is rarely or never a lottery for portfolio-entry courses and, if there is, it's not because candidates have the same number of Leaving Cert points, but because they have been awarded the same score for their portfolio, and that turns out to be the cutoff portfolio score for entry into the course in question.
Is the system corruptible? In theory, yes; the college offering the course could have a portfolio assessment system in which assessors know the identity of the candidates (i.e. portfolios are not anonymised) and they could award higher scores to candidates that they know, or want to favour for other reasons. But, even if this were to happen — and we have no reason to think that it does — Mummy and Daddy knowing the head of the department would be no help unless the head of the department (a) is also the assessor of little Tarquin's portfolio (which is unlikely; department heads have better things to do) or (b) conspires with the assessor to award Tarquin an inflated portfolio score. And conspiracies of this kind are dangerous to the participants, since they can easily become unstuck. The head of the department may have a reason to favour little Tarquin but the assessor has none, so he will have to be bribed or bullied into co-operating, and any attempt to do that creates obvious risks for the head of the Department.
It's difficult to prove a negative, so we can't say categorically that there is never any corruption in the process. But SFAIK there have been no complaints of, still less evidence of, corruption, and on the whole it seems likely that this rarely or never happens. The head of the department would jeopardise his job and his professional reputation by asking the assessor to favour a particular candidate, which seems a lot to risk just because you are socially acquainted with Tarquin's Mummy and Daddy.