It won't "fix" the non legit sample library you have. The timeout is because you don't have a license for the library...unless you've converted it from an old format (like Giga/Akai)--in which case, the full version of Kontakt will allow that w/o timeout. But, if it's a Kontakt lib? Nope. Still have to buy whatever that is--it won't time out the player once you've registered your purchase.
I don't have much of a use for the full version, honestly. I PLAY instruments...I don't edit sample mappings and attack envelopes, etc. I pay a lot of money to have the shiznit done for me by the sound designers making the products.
But, if you're into sound creation/mutation, by all means get the full version.
I also thought I would need it for Akai/giga compatibility...but, honestly, I have no use for those old sounds now that better emulations are available. Plus, the Giga converter in Kontakt BLOWS chunks. I don't think I've imported a single thing that imported correctly. That's nice that they give the player that ability (though timed out) to remind me how little use I have for the old sounds I paid so much for in the day.