That's a good question. I asked it myself when I started slinging regularly over the mobile data connection on my tethered phone (10 GB cap).
Does the slingbox transmit packets, info, etc... (use bandwith) when I am not viewing it via my desktop slingplayer?
Yes, but only a tiny bit. Slingbox communicates on it's own with the servers that manage the SlingID service once in awhile. It does this to make sure the external IP and port are up-to-date to help with remote viewing, and it happens in the background even if nobody is connected/watching the Slingbox. The amount of traffic generated by these updates is extremely small, I think you can safely disregard this with your bandwidth concerns.
Also note that viewing over the LAN at home doesn't count against your ISP bandwidth cap. The data traffic for the video stream in this case stays inside your house behind your router. It never goes out over the public internet, so you don't have to count that. Slinging only affects your 250 GB limit when you (or someone you give the password to) is remote viewing over the internet away from home.
If it only transmits while I am watching it, I shouldn't have a problem.
I don't think you're going to have a problem. But it's wise of you to keep an eye on things at the start. Here are some numbers that might help:
Based on 250 GB/month, Slinging at sustained bitrates of...
1000 kbps = 0.45 GB/hour = 555.6 hours = 23 days = 18.5 hrs/day monthly
2000 kbps = 0.9 GB/hour = 277.8 hours = 11 days = 9.25 hrs/day monthly
6000 kbps = 2.7 GB/hour = 92.6 hours = almost 4 days = 3 hrs/day monthly
Unless you have wicked fast upload speeds with your Cable service, I'd expect remote viewing bitrates well below 3000 kbps. I have Comcast, I tend to see speeds around 1500 - 1800 kbps on a good day... it's frequently less. Your connection's performance may, of course, be different.
Finally, don't forget that you have to consider all of your internet usage towards the cap (Xbox Live, Computers, Slingbox, etc.), but I suspect you'll find it kind of tough to get near 250 GB/month.
If you're really concerned, ask Comcast customer service if they can tell you how much data you've gobbled up during your current billing cycle. If so, you could call a couple times and check. If they see you're trying to be reasonable and in compliance up front, I'm sure they'll reciprocate.
Good luck !