In the situation, assuming that a change on the TUS-LAX isn't possible, then adding the 5* wouldn't be a bad option.
I wouldn't expect them to hold the plane if seriously delayed coming from TUS, but if you were 5 min behind then possibly a good chance. Not to mention that they do require you to be checked-in by T-30, however being taken care of under the 5* program could possibly meet that requirement.
On the chance that you indeed don't make the connection, I would expect that having paid for the service then you would be more easily accommodated on the next available departure.