Is this is a bad idea, Sprint Tri with minimal prep?

Anyone can do a sprint unless there's something obvious preventing it: massively obese, severe injury etc.

You'll be fine.

If you feel you can safely complete the swim I say go for it!

If you're in decent shape and feel like you can finish, then you probably can. You can always take it easy on the bike and walk a little on the run (I know I did for my first tri) but the swim you can't really stop. You can backstroke or breaststroke for a while though.

For 61 degrees you will probably want a wet suit.

As mentioned above, if you can swim the distance, you should be fine.  Just don't underestimate it.

When I first decided I wanted to do a triathlon, I just assumed I would go to the YMCA, jump in the pool, and do a 10 lap (500 yard) warm up.  Boy was I suprised when I barely could make it 25 yards without hanging on to the wall for dear life.  This was right before I ran a sub 4 hour marathon, so I figured I was in pretty decent shape.

Swimming is more about technique and relaxing than brute fitness.

If you're concerned, why don't you see if you can swim for 400 meters?  You said you have a pool, and while open water swimming isn't exactly the same, if you can swim 16 laps in the typical distance pool, then you can reasonably infer that you won't drown.  It kind of makes sense to practice how you want to race...

61 degrees is incredibly cold to someone like me who lives in the south, but I guess it's all relative.  I'd get a suit.

61 degree water is COLD. Do not attempt without a wetsuit. Especially as air temps in the Pacific Northwest are not likely to be high either if it's a morning start. Last year I pulled out of a swim in supposedly 61 degree water, 39 degree air temps. I'm a very experienced swimmer, and had a full wetsuit. Just wasn't comfortable with it as I hadn't trained for those conditions, and became so chilled on a practice swim I couldn't handle transition or bike safely. Granted, I'm scrawny and a cold-water wimp, but still, 61 isn't warm.

The main issue is the swim. It sounds like you have great bike fitness, at least endurance, and a passable run. If you can comfortably swim the race distance in a pool, without a wetsuit, then go for it (but with a wetsuit in the race). Please don't depend on your wetsuit as a flotation device. You need to have a good level of comfort with the distance, open water, and the wetsuit prior to the race. If not, work on your swimming and choose another race when you are ready. 

Does this happen to every runner?

I tried doing a long sprint without being completely ready for the swim.  I bailed on the swim though after a couple minutes.

Take a 400-500 yard practice swim or two at local indoor pool, and try an OWS with a buddy in a kayak/canoe before trying this for first time on race day.  Recommend wetsuit at that temp also.

at 61 degree water, you may want to get some silicone/wax earplugs (only about 2 bucks at Walmart). Reason is that below 65 degree, some people will experience some dizziness/disorientation from the cold water getting into the ear canal after a little while. It happened to  a few, including myself, in our tri-training club this spring while doing OWS training in 62 degree water.  No one has same problem once we all put in ear plugs.

Have a great time.  You'll always remember your first!