Can the phrase "to be able to" be used without the preposition "to". For example, can you say "I will call you back as soon as I am able?"
Yes. The 'to' is part of an implied infinitive, meaning "I will call you back as soon as I am able to call you back". If context is understood (in this case, you have already stated that the intended action is to call back), the preposition is not necessary.