I think this would create a lot of interest in the start-up area. As part of my course there was a compulsory 6-month placement in industry. Most of the students were blissfully unaware of the start-up opportunities available, especially when the big players were dangling large money incentives and holding big promotion events. Also, if you took a typical internship with a bank, etc, the chances are that you got offered a graduate job. This in itself would prevent a lot of the students looking further for other opportunities even if they were being promoted.

The only time I even had a hint of the start-up world was the odd email from the career officer. (I actually remember the SongKick advert. I was really tempted to apply, even though you were just looking for a graduate position. In hindsight, I should have tried my luck :))

What would be useful in promoting the internships would be a start-up demo-day, where bunch of start-ups would come in and showcase their product/vision, development technologies, and any other 'cool stuff'.

Edit: To clarify, rather that a start-up fair, where students stumble about, the demo-day would be contained in a lecture room with a proper presentation and QA session. These types of events were always packed in uni.