In line with Government Policy, the process for making appointments to State Boards has, since mid-2011, been administered through the Public Appointments Service (PAS). PAS publicly invites Expressions of Interest from all interested parties, including those of the type referred to in the question. These applications are not categorised by reference to the occupational background of the applicants within their own organisation or on whether they form part of the Irish diaspora.
In parallel with the formal system administered through PAS, I occasionally receive expressions of interest directly from individuals for consideration for appointment to State Boards. While the occupational background of these individuals may not be explicit, I am not aware of any multinational executives having expressed interest through this channel. In all cases, however, any such applicants have been referred to formal process administered the Public Appointments Service.