Swimming

ok so. advice needed here. I might have accidently agreed to take part in the Virgin London triathlon. I will be doing the 1500 metre swim. in the thames. I was last in a pool 4 years ago. have only ever been in the pool when I was younger and that was always mucking about not actually swimming.
my question? is it realistic that I can be train myself up to do 1500m in time (31st July) without: any prior experience of proper swimming, no formal lessons (either prior or planned), any good swimming style (tend to use arms to pull and no good at using legs to push), very little time to actually get to the pool between now and then (once maybe twice a week)