Well, I know this is what Bob, Jr., believed. The 7 page letter from Rice to Jones on the 1971 split is in the John R. Rice Papers at Southwestern BTS. (I have done research there and have a digital copy.) I also know grads from those years who agrees that this is what Bob, Jr., preached. Rice wrote on p. 5, "You did not agree with my position that there is no way to know when the end of this age approaches. And, as you said plainly, you do not believe that great area-wide revivals are possible now in the same sense as in other days because you think we are approaching the end of the age."
Also, in the same paragraph JRR points out that Jones did not allow his book, We Can Have Revival Now, to be sold in the BJU bookstore. That is ironic, since the book is a series of lectures at BJU in 1950!
Beyond that, I don't think Bob Sr. held to this. I don't know about Bob III or anyone else. The students, if not the school, are mostly Baptist, so that may have played a part in the fact that many grads believe in the possibility of revival.