Answer is yes, it can. Here's how.
Structural Deficit = Total Government Deficit -- Cyclical Deficit -- One-off Measures
(One-off Measures are emergency spending, one-off banks recaps etc)
So Structural Deficit = Government Deficit that would have prevailed if economy operated at 'full employment' (full capacity)
What is Cyclical Deficit in the above?
Cyclical Deficit = Output Gap * Elasticity of Fiscal Balance
Output Gap = Potential (Full-Employment) Output of Economy -- Actual (realised) Output of Economy
Output Gap is expressed in % terms difference.
Elasticity of Fiscal Balance = 0.38-0.4 for Ireland and captures the percentage change in (Government expenditure net of Government revenue) per 1% change in output gap. DofF estimates this to be 0.4 and EU Commission estimates it to be 0.38 for Ireland.
Thus, from Equation 2 above:
Cyclical Deficit = [Potential GDP -- Actual GDP]*0.38
for EU Commission, or replacing 0.38 with 0.4 above gets you approximation for DofF model.
Now, economic growth can happen at the point above 'Full Employment', in which case Output Gap will be negative, as potential GDP will exceed actual GDP, giving positive output gap - consistent with economy overheating.
Alternatively it can happen at 'Below Full Employment', so that output gap is negative (economy growing without overheating).
If growth happens when economy is overheating, in the equations above, cyclical deficit becomes positive, in other words, there is actual deficit. If it is happening in the economy that is not overheating, then cyclical deficit is negative, so there is cyclical surplus.
Now's for an interesting bit: both the EU Commission and the DofF estimate that in 2014, despite the fact that we are expected to run double-digit unemployment, Irish economy will be technically in 'overheating' or 'above full-employment' mode. This explains why even with shallow growth, in 2015 Ireland is still forecast to run 3.5% structural deficit (DofF forecast, which is ahead of 2.5% structural deficit forecast for the same year by the IMF).
In other words, if we hike growth even more, in 2015 over and above currently assumed by the DofF, so that our output gap will rise by 1% in 2015, this will result in an increase in Cyclical Deficit of 0.4%. This will result in subtracting a larger negative number in computation of Structural Deficit in the first equation above, thus increasing Structural Deficit.
In other words, if growth happens when economy is considered 'overheating' and that growth does not increase potential output of the economy, but only transient output, then such growth will increase, not decrease Structural Deficit, unless the state somehow taxes entire growth*0.4 out of the economy and does not spend the collected amounts. This can be done if we were to run a cash-based sovereign wealth fund that will not invest any of its proceeds back into the economy.
Logic? Who said economics supposed to have real world logic? Not me...