If you took a mortgage for €100,000 @ 4.5% you would pay interest of €4,500 in the first year and you would be allowed to set €3,375 against the income from the property therefore saving about €1,850 from your tax bill (assuming you pay at the higher rate), so the cost to you of the mortgage will be €2,650.
If you are therefore leaving €100,000 on deposit at 2% you will get €1,180 after dirt.
I don't think it makes sense to spent €2,650 to gain €1,180.
It might make sense if you had something better to do with the money than leave it on deposit or if you were likely to need to borrow at a higher rate than the mortgage for something else (eg car loan).