Don't think so Rapparee, here are the details related to the mention of first use of machine guns during the Easter Week Rising:

From RTE Chronology of the Rising.

Remembering and taking note of the fact that the fires in Sackville Street started around 20:30hrs in the evening of the 24th April, 1916

Tuesday, 25 April, 1916

• 02.15 – Capt. Elliotson and an army machine gun group of 100 men secure Shelbourne Hotel which offers them military control of St Stephen's Green.

• 03.20 – Troops take control of Royal Services Club on St Stephen's Green.

• 03.45 – Brigadier Lowe arrives at Kingsbridge with remainder of 25th Reserve Infantry Brigade and takes personal control of British forces.

• 05.30 – Intense gunfire around Stephen's Green under fire with high numbers of rebel casualties.

• 08.00 – British forces take control of City Hall having re-captured the roof. All rebels remaining in the building are taken prisoner.

• 08.30 – Under heavy fire the Citizen Army force at St Stephen's Green take the decision to abandon their exposed positions in the Green and take up new positions in the Royal College of Surgeons. They take to the roof and begin exchanging fire with British forces. Four rebels are confirmed killed in the Green.

Maximum range of that ammunition was only 350 yards by which time the "tracer" material would have burned itself out. As the crow flies the distance from the Shelbourne Hotel to Sackville Street is more than 1,250 metres.

The geography is also wrong for any fire from the British gunners positions firing into Stephens Green for any stray rounds to land in Sackville Street. From the Shelbourne Hotel which lies on the North side of Stephens Green the gunners would be shooting to the South (Stephens Green) and to the West (College of Surgeons) - Sackville Street was located on the North side of the Liffey.