My BK set-up isn't doesn't allow easy use of a immersion chiller, so I have a bucket I use for chilling. More than once I have had water leak from one of the connections into the cooling wort, without any noticeable ill effects. As others have said, not ideal but probably not a big deal.
As a FWIW, I have to partially dismantle my two chiller set-up after use, and have come to the conclusion that with plastic tubing and hose clamps, it isn't wise to re-clamp the same section of tubing more than once or twice as it just doesn't seal worth a damn, so I cut off the used section of tubing after every use or two.