There is always the possibility that they will consider Mary as good for the optics but not really one of them (an ex-Prime Minister) and thus either not a real heavyweight who might pursue an independent agenda and pose a threat to theirs, or as too much of an unknown quantity.  

If they take the former view - that she is good for the optics but not a threat to their designs - they might very well appoint her - and might also be in for something of a surprise as she has a track record of pursuing a very principled line.

However he success as President of Ireland was not in breeching the very narrow limits of its real powers, but in popularising the office and greatly increasing popular engagement with it.  Thus if they want someone to reduce the "democratic deficit" and increase popular engagement with the EU, they could not do better.

The question of how effective the Council would be as a decision making body on contentious issues under her chairmanship is a different matter.  My view would be that her lack of ego, good listening skills, determination not to ignore the smaller players etc. would make her a very popular and effective chair though not necessarily very popular with the Major countries who might be looking for more of a puppet to do their bidding.

notes from no w here