I think it’s going to depend largely on how well you retain information, your background, and how well you deal with pressure. Anyone here can only give you a subjective probability of passing for people that study only one month.
For myself, I am a slow learner so I probably could not accomplish enough studying in a one month time span to pass the test however I do know people that have passed the level 1 exam with one month of preparation. Some common traits among them are their ability to think extremely quickly, exceptional educational/professional background, and in general just pretty damn smart.
In the end, there’s only one way to find out…hit the books and see what happens! good luck