The short answer is “No”.
Some people think that the drink driving laws don’t apply to cyclists, and that they can legally have a few drinks and cycle home. Sadly the law in Ireland doesn’t quite agree:
A person shall not, in a public place—
(a) drive or attempt to drive, or be in charge of, an animal-drawn vehicle, or
(b) drive or attempt to drive a pedal cycle,
while he or she is under the influence of an intoxicant to such an extent as to be incapable of having proper control of the vehicle or cycle.Road Traffic Act 2010, Section 6
If a member of the Garda Síochána is of the opinion that a cyclist has committed this offence, they can arrest them, and they will be liable to a summary conviction and a fine of up to €2,000.
Of course, the definition of how drunk you need to be to be “incapable of having proper control” is a bit subjective. Unlike the motoring offence, there appears to be no definition of the amount of alcohol in your system.
Note: this post does not constitute legal advice