IMO it’s not necessary to ‘start’ on a single speed before riding fixed- the main danger with riding fixed is, as mentioned above, overcoming the ‘stopping pedaling/coasting’ instinct, as, any attempt to coast on a fixie will most likely lead to being thrown off.
But plenty of people do ride fixed and never get thrown off- it’s not that dangerous if you go about it the right way.
Which is, find a empty car park and pedal slowly, until the ‘coasting’ instinct goes away.
That’s what i did, and, in the few months I spent riding fixed, never came close to coming off.
Just a couple of days practising that and you should be good to go, certainly nowhere near learning to unicycle in terms of difficulty.
Interestingly, a decade of riding unicyles regularly, which, obviously are also fixed gear, does nothing to prepare you for riding a fixed gear bike, in terms of overcoming the coasting habit.
Many fixies, including my ‘charge plug’ bike mentioned above, have a ‘flip-flop’ hub, with a fixed gear on one side and, on the other, a single speed with freewheel- so you can convert from fixed to coasting by flipping the wheel over.
After a few months of riding fixed, I did switch to single speed, as, having old knees and living in a very hilly place, I changed the front cog to a lower gear, and, the amount of spinning on the downhills was just too much on a fixed- but, while it lasted, riding fixed had many good aspects.
But, as several have mentioned, including me in my initial reply, riding fixed gear bike will do nothing to help you ride a unicycle.