When you explain the situation, you need to be clear that you are very willing to cancel the vacation - the job is more important to you. Whether its ok will depend a lot on both the job and the boss, but the best bet is to be very clear that the vacation is obviously secondary.
If your job is something like sweetdana was hiring for - its a high turnover job - lots of qualified applicants to choose from - lower skill - where you are going to go immediately into training, I wouldn't ask. I just quit my job June 1st. I hired my replacement (before they knew I was leaving - I knew she'd be my replacement), she couldn't start for six weeks and I missed her by two - but because she was far and away the best fit, we were willing to wait - what I was doing was a small niche thing and qualified people don't walk through the door every day.