Again, if the search engine in your documentation were decent, I would probably not need to ask this question here. The answer probably exists, but try an find it not knowing where it is!
The answer to this question appears to be yes, at least when using the pc-ble-driver, which uses only SoftDevice. In my pc-ble-driver based devices, the (connectable) advertising stops automatically on a connection event. At least I do not see it in a sniff and I do not explicitly call sd_ble_gap_adv_stop().
The question is, when I port this code over to the nRF51822 will I need to stop the advertisement myself calling sd_ble_gap_adv_stop(). or is it automatically done when receiving a connection event?
Suggestion: Turn you offline documentation into a single large pdf. A pdf has a great search engine. It might cut the number of posts to this site in half.