Is this statement true: "An increase in aggregate demand in an economy is always desirable."
No, this statement is not true. An increase in aggregate demand is often desirable, but it can also lead to inflation in some circumstances.
An increase in aggregate demand is good if aggregate supply is also rising or if it can rise with demand. For example, during a recession, aggregate supply is generally a bit lower than its potential level. In such a case, an increase in aggregate demand will lead to a growth in GDP without much of an increase in the price level.
However, if the aggregate supply cannot increase (if the economy is in the classical range of the AS curve where the curve is vertical), an increase in aggregate demand is bad for the economy. It does not create any increase in GDP. All it does is cause inflation. Therefore, the statement given is not completely true.