It is possible, but not with the ps3eye. To some extent the microphone array aspect of the ps3eye should help the mic to focus on your voice, but it's not perfect.
currently, if you plug something in to the mic input on your sound card, it is usually possible to enable "acoustic echo cancellation" on the windows recording device properties under the enhancements panel. For this to work you need to be using the mic input and be playing your output through the same chipset device. So for example on my laptop I have two jacks, 1 input and one input that both run though my realtek chipset, and it works, though I have not stress tested it.
There are pure hardware solutions. Some devices, especially headsets, use two microphones, one pointed toward the speaker and the other pointed away. The sound that is coming from the away mic is subtracted from the mic pointed at the speaker. Of course for this to work, the two microphones need to be correctly oriented and relatively close to your mouth.
If you find that vox is either issuing commands or switching to listen mode when not intended, you should consider changing your prefix and/or listen phrases. Consider also, using only one phrase for listen that is not too short. The word "listen" by itself is a poor choice. Something like "begin listen mode" will most likely get a high confidence score, and virtually no false positives.
If you use prefix mode, be sure your prefix has at least two syllables. Using a woman's name (e.g. Erika) as the prefix can work well, but may incur a very low W.A.F.