Whether or not Clarke had Nietzsche in mind when he wrote the book is a question I can't answer. I would be very surprised if he wasn't familiar with Nietzsche, though. I would also say 2001 was written and exists within the same spirit and thrust of consciousness.
The monolith is the intermediary through which the apes' begin to "overcome" their apeness and "evolve" with more "complex" uses and interaction with the world around them. The apes discover something in the world can be used to do other things, i.e., they discover "tools". This is a "jump" in consciousness and can be fairly correlated with a utilitarian expression of the will to power.
The monolith, however, could be anything. It has an exoteric existence in the world of the novel/movie, but, when push comes to shove, it is a metaphor for how consciousness seems to develop and augment over time: "outside" experience births "inside" awareness, and "inside awareness" fosters new consciousness interaction with the "outside".
In regards to Dave, the monolith becomes the intermediary for "overcoming" his present consciousness and augmenting it via being "born again" (for lack of a better phrase) as a "new child" of consciousness. The "odyssey" is both exoteric (the space voyage) and esoteric (the journey within to discover the "new child" within, which, ironically, is analogous to developing ubermensch traits).
The monolith, imo, is Clarke's symbol for an aspect of the universe "intervening" in another aspect of the universe to foster augmentation of consciousness evolution. In the sense that Nietzsche and Clarke both privilege transformation of present consciousness as fundamental to what it means to be a conscious being in the universe, I would say that 2001 can be fairly said to be of a Nietzschean vein.