In sentence 1 -- with the commas after "box" and "Austin"-- the subject is singular: voicemail box. This sentence would be similar to:
My voicemail box, as well as 70,000 other boxes in Austin, is down until tomorrow.
My voicemail box, together with 70,000 other boxes in Austin, is down until tomorrow.
The verb is singular.
Sentence 2 has a plural subject: My voice mail box and 70,000 other boxes. The verb is plural.
Sentence 1 could have the additional material in parentheses. Sentence 2 could not, as both elements together form the compound subject.