You definitely can do it! I took lessons last year and I couldn't do more than 50 meters without stopping for a long break. I probably will take lessons again after I get a little more overall fitness. But I'm now swimming 1,000 meters comfortably (although I use fins, but don't kick).

I luuuuuuuuuuuuuuuv swimming, but I'm just so terribly, terribly slow. Even the 70 year old guy swims faster than I do.