I guess no as i have seen alert signs of alligators and snake near lake shore
While I don't think it's expressly forbidden there are posted signs (one I can think of closer to the dog run) that prohibit access to the shore. I've seen people fishing from boats out in the deeper waters but they didn't launch from the park; there's a lot of private houses on that water.
Its not exactly easy to get down to the shore but i would guess probably not
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