Even if you can manage to drill a hole down the center of that 6mm screw I'd bet money that that the extractor would break.
The extractors just don't work that well for screws that small.
Better to remove the cover and use the vise grips.
+1...I'm going to try what Steve_K recommended with those Special reverse drill extractors,you'll need a strong variable speed drill, possibly 1/2" drive that has reverse.There are 6mm exhaust flange bolts that get frozen lot's of times and we need a way to remove them...,if we can get to them
w/o removing the entire cylinder head that is;some times they are just too badly seized in.I have heard good things about those Special reverse removal drill tool kits that Steve_K mentioned...and I'm going to get some of them...Easy Out's are difficult..,especially the spiral ones;I have used the square ones with"some" success in the past.....
I'm also going to get a few of the correct size Left Hand drill bits that will work for 6mm studs such as 72500john has recommended.
I've had the best results with extractors when I was able to drill straightly all the way through to the bottom of the broken stud(sometimes it's just not possible
)and that sort of relieves the "stress"...and then I'd just keep shooting PBBlaster into that hole for maybe..a few days,and then give it more patient persuasion;the hardest part for me is the "patient persuasion"!