Unfortunately, this isn't possible. The actress who provided the original LCARS and Computer voices, Majel Barrett-Roddenberry, is deceased
Unless, of course, you mean various audio clips from the series that have been touched up and adapted for use in the game.
Prior to her death, there was an advertisement on the Roddenberry website about a CD library of computer voiceovers that could be used in different productions (fan-based webisodes like "Star Trek Phase II," "Hidden Frontier," etc).
It disappeared from their website before she died, so I wonder if the idea got started then scrapped, scrapped entirely, or if it's still there somewhere, waiting to be burned to CDs.
It wouldn't kill Cryptic to contact them and ask.
That said, Kudos to Cryptic for listening to the fans and getting Chase involved - and shame on them for not giving a tip of the hat in their announcement to KirkFat's hard push on these forums to make that happen in the first place. It wasn't Cryptic's idea.
Originally Posted by http://www.startrekonline.com/node/1982
"Fans have always asked when there was going to be a game of Dabo. Cryptic's version is everything I had hoped it would be – fun, strategically challenging, and rewarding on many levels," says Masterson. "We've recorded some fun little extras, as well. I'm looking forward to hearing the fans' response."
Uhm, okay? Where's this version of Dabo then? Last I checked, the ENTIRE Dabo game could be played by a G15 keyboard set to mouse-click every couple seconds. Then you leave it overnight.