No unless you go on for days or something I'm pretty sure you couldn't die from this. Unless you have a heart condition or something. I mean what would kill you? too much lactic acid? No I really don't think so.
As for the original question. Interesting... I might actually try 15 min of this some day. Not today tough, I can't be asked...
I think the result could be more interesting than you expect. If I understood your theories correctly. Many here seem to think you will start to slow down quickly after 40 seconds or so to a really slow pace, and pretty quickly they would be lying on the ground or walking. While others seem to think that you would slow down in a more gradual way, going to 6-7 minute pace after a while, and then i guess you think you would just get slower.
Lets say the person doing this is a very fit 10k runner, who if he wanted could probably run 100 miles in 15 hours as well(or however long a good 10k runner could run). Lets also say this person has unlimited mental strength.
I think he would start too slow down very quickly after 40 seconds as lactic acid levels get too high, he might even need to walk. But then his body would start to remove lactic acid, eventually, I don't know how long it would take, but eventually I think he would start approaching, for example hm pace, and peak at that pace, stay there for a while, and then gradually slow down again, this time slowing down much slower, but now slowing down all the way untill he can't walk anymore. Ofcourse when he finaly collapses his body would be completely trashed...