Yes, the warranty is an UNLIMITED Lifetime Warranty for the lifetime of the gun, so the warranty will still be good.
Personally I stay away from anything that has been reconditioned/refurbished, firearm or otherwise. That doesn't mean the product is bad if it has been refurbished/reconditioned( just means it was once bad). Having said that, if you have gone over the gun and it is right I see no problem with picking it up assuming you have no problem with it being reconditioned.
BTW do you know what the problem with it was?