Of course you can!
Correct me if I'm wrong but I guess Gold Beach Resort is found in Flic en Flac, one of the most famous beaches in Mauritius!
Although most local public beaches have people already around, they are just as safe as any public beaches all other the world. Flic en Flac is a famous spot for walking at night. I used to do it myself every Saturday night and didn't have any probs not coz I'm Mauritian but coz there were ppl around just like me and this beach is right in front lighted bungalows and hotels, so the path is lighted and kind of safe!!
Its your duty though to do things sensibly. Here are a few examples you should try to AVOID at all costs:
1) Leave the bungalow doors unlocked and go for a walk
2) Take all the money and wear all the jewellery while walking at midnight on a deserted and unlightened part of the beach
3)Go to remote places for camping
These are just stupid things to do and thus you would invite trouble by doing so.
If this can make you feel better, there is a police station and a Coast guard station just near the beach of Flic en Flac
Hope this helps. Just enjoy your trip