No, as it does not cover the entire mic. It is designed to go between the audio source and the microphone, and specifically to stop wind noise.
What would fix the issue you're describing is either a) investing in a quieter keyboard and mouse, or b) Dialing down the gain on your microphone and speaking more directly in to it, at which point you'd want this product, as it will prevent your "p"s, "b"s, and "t"s from creating loud popping noises in the recording.
Not much you can do to prevent a microphone from doing it's job - that is to say, hearing sounds :-)
depending on if you keyboard/mouse is very loud or if it is quite, the pop filter will filter it out. My keyboard is really loud so it wouldn't filter all of it, just most of it. Quite keyboards most likely will become silent.