Probably not fail, but definitely it could cause it to not turn. - When the connection is loose you can often get enough power for the dash and ECU etc for fire-up, but not enough current to turn the starter over. I've had that before and fixed it by tapping the connections down a little harder on the terminals (obviously I tightened them properly later).
I guess it could fail if it has a series of "brown" starts (where it doesn't get enough power to turn the motor and so stalls with power going through the windings) - I'm not an electrician so when I say "I guess", I mean it.