Wayne Handley used to do exactly that in the Turbo Raven, an aerobatic monoplane modified with a Pratt & Whitney PT-6, giving the airplane a thrust to weight of more than 1. The airplane can be seen climbing vertically in this video, but it doesn't include his hovering act, which I believe he stopped doing in the late 90s because it was quite a dangerous maneuver (an engine failure close to the ground while in the hover would probably be fatal).
I've seen his hovering act at Oshkosh in the mid 90s, and he would fly along, slowing and slowing until the nose was vertical, and he would stop in a hover in front of the crowd, literally hanging on the prop, about 200 ft in the air. He would move the airplane in a box pattern, sideways, vertically up a couple hundred feet, sideways and vertically down, hover for a few more seconds at his starting spot, then accelerate vertically up to several thousand feet. It was the all time most amazing airshow act I've ever seen.
The full span ailerons provided the anti-torque control, and the rudder and elevator provided provided attitude control while in the hover. The wings are completely unloaded and are just worthless appendages, except for the anti-torque effect being provided by the ailerons.
The PT-6 version was 750 HP which will make around 3000+ lbs of thrust, and this was quite a bit more than it weighed, hence the ability to hover. You wouldn't be able to get that power to weight ratio with a piston engine so the airplane pictured in the MFS, which appears to be a regular piston powered Extra 300 or similar, probably can't quite manage it. Put a turboprop in it however and it certainly could, because the only limitation is the thrust to weight ratio.