No. Once the toy looking figurine is obtained there is no radar or any screen for that matter. They all turn pitch black preventing me from seeing any dots at all. And even after depositing the item at the oil rig you mentioned which you can find without the radar’s help, the radar and everything never show up again. For the record, I can still access the PC to check my mail, but I haven’t gotten any besides the two you start with. (I did look around the ship for any other interactions and nothing stood out aside from the usual toilet/bed/crane comments etc.)
Also I did experience something else that was an unmistakable bug. While cleaning the first object, during my first attempt out of the two I had done, the loud scraping noise of the tool that replaces the mouse cursor can apparently continue playing on a loop even after you are done. I’ve even heard it play on the main menu and the only way to make it stop was to quit the game completely and start from the beginning.