At least two of my past jobs were jobs where the employers stated range was substantially below what I was finally offered, so this can backfire. In one case I negotiated my way up 50% over the initial offer, and the initial offer was already at the top of the advertised range. In the other I got 30% above the top of the range + about twice the options. Both cases it was the situation where they realised I was overqualified for what they'd spec'ed, but they decided they wanted me anyway and upped their budget.

I know it can often mean wasting time, but focus on whether it's a company you want to work at. If it is, see it as a way of getting on their radar, and if you can't agree for that position, ask them to keep you in mind if they get something more suitable.