Can I connect a dct6200 to my comcast network?

You probably will be able to for a little while, until the headend your DCT talks back to gets around to polling it.  Polling is when the main computer checks all of the cable boxes in its' domain for channel auths, pay-per-view purchases, and other behind the scene info.  If the DCT isn't registered on the system, the headend will send a disconnect signal...eventually.  This may happen in either a couple of days, or a few days, (hedging here) depending on the polling schedule. You may also find that while the DCT is operating, initially, the channel map maybe different, if your box was from another city or state. As to whether Comcast will allow registering a box that was bought, and not rented properly through them, that is highly debatable. There's no rule I am aware of against that, however.
Good Luck,
DCT Goddess