That's done by default to stop audible clicks from happening at audio edits. Without that quick fade, sudden changes in the waveform at edit points are so abrupt they sound like a "click" in your audio.
To answer your question, yes, you may turn it off and change Vegas' default behavior:
Options>Preferences>"Editing" tab>Quick fade for audio events (ms):
The normal default is 10. Change that number to 0 to remove the quick fades from that point forward.
Leave it alone and worry about something else. @Turd is correct about the setting and the rationale for having it, however, it can't be set to less than 1 ms, so you'll always see a fade. As wjauch said, a little overlap never hurt anything. On occasion, I split within a clip and I just drag the fades back to their original states since there is no mismatch in the audio from sample to sample. If I'm awake when I do the split and the audio continues while I do something else with the video, I only split the video and leave the audio unchanged.