I have not actually used NetStumbler, but the SSID is broadcast by the client as part of its connection to the access point. It does so to make sure that it is connecting to the correct access point. My understanding of NetStumbler is that it is simply sniffing all wireless, so the likelihood is that yes, your SSID could get picked up because of the client. Unfortunately, there is nothing you can do about that.
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Ask the Expert: Disabling SSID to secure a WLAN
This was first published in July 2002