Expatriate Forums in Japan

I just applied for a renewal of my visa. However I only have to stay in the country for a a bit motre than a month from now. On my stamp for visa in prosess I am allowed to stay untill I leave the country (not to come back in any near future).

So what I'm wondering is if I can just leave on that stamp without going to pick up my new visa (which would save me that hustle + the visa costs). What do you think? Could I be in trouble at the airport if I did this?