The only way they can qualify right now to TI, is if they will be invited to participate in the event (special entry). It is not in the rule book or anything but they are hoping if that will happen as they are the reigning champions.
I do not think that they'll have that special entry. Maybe if Valve does, they can surprise the world and have them direct invite if they will not be able to get into the TI qualifier. The decision is in hands of Valve if OG will be beaten through that qualifier.
There's no last hope but only that qualifier so if Valve gives meaning a lot for OG, they'll have their own rule that shall be announced and give them the special treatment. But it was stated already before by Valve that they're going with the rules and that's why there were majors and minors but OG didn't qualify for those.