I think that any assessment of the new testament as a source is always based on your own particular bias. If you are an avid christian, you will accept the its value to the extent of the depth of your faith. It is hard to be objective about the one source that validates your belief. If on the other hand you are an avid athiest you will reject the entire thing.
I have two points to make, one is that there may have been more than one itinerant cleric who went around turning people away from the influence of Rome's paganism and the extreme orthodoxy of the temple. A more moderate type of propagandist if you like. My feeling is that as there are no records of a trial from the Roman point of view, and we have to remember that the Romans were almost as meticulous as the nazis about keeping records, we can assume that if a trial actually happened, it was a local event. Crucifixion was the standard Roman method of dealing with insurgents so possibly, there was a trial and possibly there was only one person.
My second point is that the bible is not complete. When the books were assembled to be used as the guide to christianity, the people who decided which were going to be included and which not, could only have done exactly what publishers of early times did with every written work. How do we know for sure that was is left off at the end of Herodotus wasn't thrown away because it cast Athens is a bad light. The same thing can be said about Thucydides and other writers who have bits and pieces missing and if we go by the style of writing of the day, Suetonius' tabloid style for example, writing of the time was extremely biased in favour of the subjectivity of the writer. There were no professors to correct what was written to bring the writer back on track and to point out the lack of objectivity. So except as a source of more or less what life was like at the time, and as an example of the writing style of the time, just like all the other writers, I think the New Testament can only be used to lend credence to Josephus and Josephus to lend credence to the Bible.
Sorry it's a long waffle but the answer to this question can only be that it depends on your subjectivity.
For my part, I wouldn't use it unless I was researching something that was absolutely not mentioned anywhere else but then I would do it with a lot of skepticism.