No, it is often not true. An increase in demand can be very destructive socially, morally, or in human costs.

An increase in guns means an increase in fear and insecurity. In private hands, it means an increase in murders. In government hands, it means an increase in war is likely going on, about to happen, or feared to happen. Either way, it means a loss of resources that could be devoted to almost anything that would be better, such as education, infrastructure, and so on.

An increase in alcohol or other drugs likely means an increase in human misery, overdoses, early deaths, and crime. An increase in pornography could be positive in the sense of less censorship or taboos on talking about sex, but it likely is negative in meaning more human trafficking, problems with body images and expectations about sex, and dehumanization of women.

An increase in demand is usually environmentally destructive. An increase in demand is also usually morally destructive, meaning more crass materialism and greed.

An increase in aggregate demand--a shift of the demand curve to the right--is generally an indicator that the economy is strong, and will continue to be so in the near future. This is because an increase in aggregate demand indicates that consumers have the means to consume more goods and services, which producers meet by producing more. The producers employ more people, and the economy is thus more healthy. So usually, increasing aggregate demand is a indicator of a healthy economy, and this is why Keynesian economists focus on trying to boost demand via fiscal and monetary policy during economic downturns.

But an increase in aggregate demand is not always a good thing. If, for example, producers cannot meet aggregate demand, inflation and shortages can set in, both of which can lead to economic downturns, and, apart from theoretical issues, create problems for people who live through them. We should also remember that unfortunate events can cause the demand curve to shift to the right, like wars and natural disasters. In these cases, the increases in aggregate demand are certainly not good for people, and possibly not good for the long-term health of the economy. So it is clear that this statement is not always true.

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.