it will run out of std turbo before you run out of fuel
if you up boost to 0.9 it will still be running well rich ,not lean - run more on the stock turbo and it will break. so to realise the benifits of the boost you'll need a piggyback ecu at least to lean it off.
From what i'm lead to believe, any 'radical' mods to a Skyline, the standard ECU will chuck fuel in bigtime as a failsafe.. this happened to my R32 after i did a few things to it before fitting Power FC..
the stock rb20 turbo has a ceramic exhaust wheel, the general consesus is that this will break due to a combination of heat and revs if you run 1bar (some say anything upto 1 bar is OK). I'd say the safe limit allowing for hot days and cold days is 0.9bar (std is 0.8ish).
at this level of boost the factory ecu will dump alot of fuel in for safety and you'll get crap fuel consumption (i got ~10mpg!) so running lean wont be a problem. the other side effect of running so rich is that you lose a fair amount of power.
so to correct the fuelling you can either fit a piggy back ecu like a SAFC and trick the factory ecu into supplying less fuel or get a mappable full replacement ecu like a Power FC or as bigblue and martinc say get your factory ecu "chipped" or "rewritten" - personally i dont know anyone in the UK that does this for the r32gtst - and i would want to get any "off the shelf" map checked on a dyno as every car is different.
its only once you have a mechanism to fix the fuelling that you need to watch out for running lean and causing damage.