1

If an attacker gains access to a cell phone's text messages, and that user routinely used text messages to receive 2-factor tokens can this information be used to gain further access to the persons accounts?

2

In the short term, the tokens obviously expire very quickly, so if your attacker has only had once off access this isn't a problem. If your attacker has live access to your phone's messages as they come in, then they can request a new token themselves and use it immediately to pass authentication before it expires.

With only a history of tokens, it is possible (with difficulty) to figure out the backing pattern that makes your authenticator unique, and predict future tokens - however the algorithms behind these systems are designed to make this impossible or infeasable without first analyzing many thousands of past tokens.

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