Early in my career I applied for a job that stipulated 2,000 hrs and I had close 1,000, but all on a type they operated. It was a white lie to get through the initial online screening. At the same time I still had to upload my cv which stated my exact hours (screened by a human). I did it on the advise of a senior training captain I had flown with.
I was called for a 2 day selection and the first thing they did as standard was to check logbooks and licenses... It was never questioned until the stage of job offer (and even then they just requested that I had hours required by company manuals when joining which was still 500 less than those stated in the job advert). They happened to be real short of rated, current, experienced and available guys that year.
Sometime later the airline became more desirable and they increased the hours required to 4,000 min to apply. Guys from my previous crowd now couldn't get a foot in, who as it happened went bust quite soon after.
So yes, it does happen. I took a calculated risk that paid off, but I certainly wouldn't try it with the bigger operators. You will be leaving the recruitment centre in short order and will probably loose your one chance with them.