I used to night fish for large lmb in the summer there all the time and never had any issues and would see many other boats out there way after hour's as well. It's at a different entrance than the park/picnic/swimming area entrance which is gated and closed after hours.
The whole state park itself is hundreds of acres and surrounds the entire pond.
Word of warning. Burr Pond has many stumps and logs barely submerged including in the middle and I highly suggest you would only use a your trolling motor at night.