The answer has been known for decades. There are numerous examples of similar things happening.
Some people on this board may have heard of the Millerites from the mid-19th century, who believed that they had calculated the exact year, month, and day of Christ's return - conveniently not too far away in fact. So they went out into the countryside to meet the Lord and ... nothing happened. Undaunted they reworked their calculations, found that they had made a minor error, and proclaimed a new date that was also, conveniently, not too far in the future. And so it went through several iterations.
This has all been very well documented with many such groups over the years - reaching such a date won't stop the predictions, it will just mean that the predictions will be reworked to a new date.
So I wouldn't predict that reaching Feb 4 or even Dec 31 of this year without anything happening will discourage the jihadis in the slightest - they will simply declare that they had made some minor errors, the time wasn't right, etc, etc. Yeah, right, talk is cheap, and we've heard a lot of it lately. Actions actually cost and mean something, but merely making bold words means little.
The big difference between the Millerites and the jihadis is that the Millerites went out in earnest prayer and humbleness to meet their Lord. The jihadis want to take celestial matters into their own hands ... much like a certain other angelic personage is said to have done, and who was banished from Heaven for his trouble.