I can only speak about the cruises that I have been on, and the answer is yes. I have usually cruised with my partner, but on the occassion that I took my Father on a cruise, as a single person, I received an invitation on the second day to a get together in one of the public rooms in order to meet other single travellers onboard. I do not know what dining arrangements you have made, but if you have arranged to sit at a table of eight or ten, then you will probably find that you will not be the only single traveller at the table. Happy cruising.
Royal Caribbean - X-mas Cruise 2007: I was a single traveler, was placed with one Dutch couple (no one else) on a table for 10 on the fringe near the entrance on a pedestal the first night, the couple did not show up the second and third nights, and I was left by myself being stared at by everyone. I did not go eat in the dining room after that.
Burrows is absolutely correct.