Yes, you absolutely could do it. I spent all summer working on my swimming, and I honestly think the only thing it did for me was give me the guts to get in the water. It certainly didn't actually help me with the swim portion, as I wound up doing backstroke for most of the way.
I never once did backstroke in my training. I think my problem was two-fold: One, I'm very OCD and when I was swimming laps I would count my strokes. All the time, every time. During the race, I couldn't get past 5 strokes or so without kicking or being kicked, so that threw my count off and therefore threw off my whole rhythm. Thus, the backstroke. Also, even though I swam in a lake several times during the summer, I guess I didn't get enough used to the serious differences between pool and lake swimming and just couldn't bring myself to do it very long in the actual race. So, all that is to say, despite my best efforts and lots of training in the pool, I really don't think I used any of it in the actual race.
Now, with the bike and the running, it was so very obvious that the training paid off. I did so much better on the bike than I thought I would that my whole family missed me coming in.
And, as it always does, running goes so much better with lots of miles under your belt.
So, all that is to say, I think you should do it! I had so much fun in mine and will always be so glad I did it! If you know how to swim at all (even if you can't train for that part) and you run, bike or do whatever else you like to do for exercise, you'll do great!
Leslie
PS - just re-read your post - the swim part of my race was 1/2 mile, with a 12 mile bike and 3.1 mile run. That's pretty standard for sprint triathlons, although the swim part is often shorter than that. Go for it!