The hard-science answer: no
If you go to the wikipedia page on this sort of propulsion, Ionocraft, which I arrived at with trivial effort by googling "air ionizing movement", you find several piece of information
In its basic form, the ionocraft is able to produce forces great enough to lift about a gram of payload per watt.
Most ionocraft cannot lift their own powersupplies. A 80kg human being, by this metric, would need 80kW of power. An 80kW power supply weigh substantially more than a human being, so would require even more power to lift. Technically they could generate some lift, but it would be so minuscule compared to virtually every other force involved in flight or landing that you wouldn't even know they turned it on.
Further reading of the wikipedia page gives you the formula for how much force is generated by such a system:
$$F=\frac{Id}{k}$$
Where F is the force, I is the current, d is the distance between annode and cathode, and k is a constant for air (Nominal value $2\cdot10^{-4} m^2 V^{−1} s^{−1}$)
Given that we know how much force it takes to hold a 80kg person aloft, $F=mg=80kg\cdot9.8m/s^2 = 784kN$, what we're really trying to figure out is the current needed. If we rearrange the formula, we get
$$I=\frac{Fk}{d} = \frac{156.8}{d}$$
Where d is measured in meters. This shows the real limit of such propulsion: propulsion goes down as the distance between the anodes and cathodes goes up. To maximize propulsion, you want them to be as close together as possible. However, there's a problem. Too close and the corona effect used for thrust is replaced by lighting style arcing! You can't get much above 30kV/cm, and even at that point you start losing lift due to corona streamers. However, we have to increase the voltage to increase current! It's a catch 22.
In the end, what you really need is more surface area. Actual lifters that have been made in labs might lift upwards of 0.5kg over a square meter of lifting surface. That means our human is going to need 160 square meters of lifting area to lift their weight. That's about the area of a volley ball court!