Either way it's not connected to the house ground. Doesn't matter.
Floating ground is a phenomenon where a circuit's ground have a differing, usually higher potential than earth's ground.
In a properly isolated system floating ground is usually fine, as it doesn't get into contact with human.
But in a metal chassis, this means if you're grounded and you touch the chassis, a current can flow through you to the ground.
0.1 mA can be felt like a localised tingling or very small vibration.
0.5 mA can feel tingly and the sensation like it spreads under the skin.
1 mA is painful.
10 mA muscle spasm.
100 mA is entering dangerous ventricular fibrillation category.
A well designed SMPS (by definition should be a circuit isolated from mains so for simplicity we can say a minimum risk of ground fault) should have their ground close to neutral, so even if they are floating, the hazard is minimal. In fact some smaller wattage SMPS doesn't have ground input.
Some cheaper supplies is not, however, like those you'd find for led drivers or even diy CNC/Plotter/3D printers. These needs high power, low quality output (ripple wise) so expensive designs is usually out of spec. These need to and must be grounded at all times.
Because if you think about it, to have 0.5 mA run through you, a normal human with like, anywhere from tens to hundreds of kOhms resistance, it only needs floating ground potential of 10 to 50V to start feeling tingly.
A little related fact, powdercoating makes your metal chassis non conductive btw.
