He has a chance, sure. Hard to say exactly how much given he'll be stepping up in weight and Crawford hasn't been in a fight as difficult as this for a while - plenty of variables. In the last year or so? Yes. Overall? No, I don't think so.
Crawford feels the heat for three or four round and cracks the code. Taylor would get stopped around the tenth.
Right now I think Crawford has just that bit much for Josh, but... 1) Taylor will be best test for Crawford since Postol 2) TTT will have a decent enough start finding decent midrange and getting some bodywork off and negating Crawford's reach 3) Bud will adjust around 4/5 and start to time Josh better and keep him on the outside where he has the reach advantage. 4) Josh will still be dangerous and would not be surprised to see Bud have to get through some adversity in spots and get the chin/gut-test as yet other fighters have not been able to impose on him. One thing is for sure, Josh will put it all in the ring 100%, and as special as I think Josh is, Bud is also special, but also physically bigger with longer reach and equal / better skills in all departments. The only thing I currently think Josh has over Crawford is the intangibles / gut / heart, but I don't think that would be enough. Personally, I don't think any boxer is wise to go from 140>147 and go straight up against Bud, that is not sage advice, and I hope that Josh does not agree to this, and moves up sensibly, having at least 1 or 2 tune ups at the weight to bed in.