It would be to their advantage to call the GT, it would help them to explain the reduction in numbers and the lack of printed material.
The July 2015 Watchtower introduces a whole new idea of what will be required of JWs during the GT. It tells them that they will be required to be obedient to the Governing Body (Christ's brothers) and that they will need to make some sacrifices, with the only sacrifice mentioned being that they will have to give up their material possession.
Their problem is that the start of the GT is supposed to be marked by the UN destroying false religion, I don't know how they would explain that away.
Here's the comments in the 2015 July Watchtower
What will happen after the destruction of false religious organizations? It will be a time to reveal what is really in our heart. The majority of mankind will seek refuge in human organizations that are likened to “the rocks of the mountains.” (Rev. 6:15-17) Figuratively speaking, however, God’s people will flee to the refuge that Jehovah provides. In the first century, the interval was not a time for a mass conversion of Jews to Christianity. It was a time for action and obedience on the part of those who were already Christians. Similarly, we cannot expect that the future interruption in the great tribulation will result in an influx of new believers. Rather, it will be an opportunity for all true believers to prove their love for Jehovah and give their support to Christ’s brothers.—Matt. 25:34-40.
8 Although we do not fully understand all that will happen during that time of test, we can expect that it will involve some measure of sacrifice. In the first century, Christians had to leave behind their possessions and endure hardships in order to survive. (Mark 13:15-18) To remain faithful, will we be willing to experience material loss? Will we be ready to do whatever is required of us to prove our loyalty to Jehovah? Just think! At that time, we will be the only ones following the example of the ancient prophet Daniel by continuing to worship our God no matter what.—Dan. 6:10, 11.