What kind of connection? Wifi or ethernet? It PROBABLY doesn't make a difference, but bad airport cards have been known to cause kernel panics.
The first thing I'd suggest though is updating to 10.6.8 unless you have a specific reason for staying at .7. A lot of times Apple includes fixes for things in point releases they don't bother mentioning in the changelog. So there's at least a possibility that your issue was resolved in 10.6.8. If you ever plan to upgrade to 10.7, it'd also be a good idea to have 10.6.8 installed.
The other possibility that springs to mind for your issue however, is bad RAM. Usually the symptoms are a bit less specific, but bad RAM can have a number of odd symptoms. If you run AHT off of the Applications DVD that came with your unit and tick off the extended test box, it will do a simple memory test on your RAM.
Hi,
We have a 27' iMac running Snow Leopard 10.6.7 and each time we try to eject a server drive from the desktop to dicsonnect from it, it causes the Mac to kernel panic.
Apart from this, the Mac is working perfectly.
Has anybody seen this problem before ?
Many thanks

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic