Any GTA: LCS that one can use to downgrade with will NOT be a "greatest hits" version. However, I can't say for sure if all non-greatest hits will be be usable.
The best way to check is to pop it in and see if it comes with the v2.0 update.
I was one of those idiots who only too happily upgraded upon recieving his PSP. Two weeks later DaX came out with a downgrader and I had the happy pleasure of travelling 118km on public transit (NOT greyhound, actually going from city to city with different local transit systems) and across international borders to get my hands on that specific version of GTA:LCS for it.
If you ask really nicely and live in Vancouver B.C., I might let you use it
