Yes, the transaction will still be present in the log. The log is a recording of all transaction data in historic order, organized for efficient access. But I would be highly skeptical of this affecting your overall performance/size significantly, and only in reads of the log. Could you help me understand what your underlying concern here is when you say "database growth issues"?
Perhaps it would be useful to have a call to discuss the specifics of your use case. If that's something you'd be interested in I can setup a call with members of our team, just shoot me an e-mail via email@example.com or firstname.lastname@example.org.