It might be possible, but unlikely to take. Apes have one more pair of chromosomes than humans (48 for Apes, 46 for humans). If an offspring were to survive it would be sterile as it would have an odd number of chromosomes thus would be unable to pass along half. It’s rare when you can produce offspring from a mismatched pair. Of course mules (mix of horse and donkey) are a result of this but in most cases it’s very rare.
There are many definitions of what kind of unit a species is (or should be). A common definition is that of a group of organisms capable of interbreeding and producing fertile offspring of both genders, and separated from other such groups with which interbreeding does not (normally) happen. Other definitions may focus on similarity of DNA or morphology. Some species are further subdivided into subspecies, and here also there is no close agreement on the criteria to be used.
Big cat hybrids have been known to be occasionally fertile (probably on account on both species involved having same number of chromosomes), so any hard and fast definition of species will either have to acknowledge this or lump what were once separate species into much broader ones.
Hence the ambiguity in the definition posted above. But in general it is a definition that works well enough, and in the case of humans and infra-human primates it is iron-clad.
It’s a sick sad world. I’m sure plenty of people have fucked monkeys before, and the end result is raging AID’s, or a whole buncha blisters and maggots on your privates.
I would advise against this, but ya know that’s just me.
If it were possible, don’t you think some drunk college students would have required it as part of the hazing process for those poor wannabees pledging their fraternity?