Let me put this in a different frame. First recall that magnetic fields also store magnetic energy:
$$
E_{mag} = \int_V H. B\, dV
$$
Now, from Lagrangian mechanics, note that:
$$
L = U-V = E_{mag}+E_{grav}-\frac{mV^2}{2}-\frac{\omega^TI\omega}{2}
$$
And let's forget some dissipative effects and the angular terms for now.
Recalling Euler-Lagrange's equation:
$$
\frac{\partial L}{\partial r}-\frac{d}{dt}\left( \frac{\partial L}{\partial \dot{r}} \right)=0
$$
And understanding that the energy terms do no depend upon the time-derivative of the generalized coordinate, we have:
$$
\frac{\partial E_{mag}}{\partial r}+\frac{\partial E_{grav}}{\partial r}=m\dot{V}
$$
No news there, the gradient of the gravity potential energy is just the gravitational force everyone here knows well about. The new term, which intuitively we think could provide some orbit control is the derivative of the magnetic field:
$$
\frac{\partial E_{mag}}{\partial r}=\frac{\partial}{\partial r} \left[ \int_V H. B\, dV\right]
$$
Now, this terms represent the instantaneous rate change of magnetic stored energy per unit of length in the position of the spacecraft. So, this disregards changes in attitude of the spacecraft (we know well the effects of magnetic torques on satellites, and dropped any attitude related coordinate before). Thus, we can assume that the magnetic induction field created by the satellite ($B$) is independent of the spacecraft position. So:
$$
\frac{\partial E_{mag}}{\partial r} = \int_V \left[\frac{\partial H}{\partial r} . B\, dV\right]
$$
And the Earth's magnetic field on its orbit $H$ is not constant over space. Right? Well, I'd like to find a better reference to this value, but picking to this paper ate 324km (which is very low for an orbit) You get at most 0.16nT/km gradient vertical in a magnetic anomaly. Thus, converting to SI base units, we're talking about $1.6 \times 10^{-11}$ T/m. Dividing by the magnetic permeability of vacuum we get 0.042 A/m². So to get the same the average thrust used by GOCE (which I'm assuming around 2mN), we'd need 2mN = 0.042 A/m² * B, resulting in B ~ 47T. Sounds like much to you?
Well, incidentally I had the hunch but not a reference to tell you if this value was big or not. My google search however tells me that the record holder for world's strongest magnet as of 2019 produces "only" a magnetic flux of 45.5 T.
Remember when people tell you not to bring metal objects close to an MRI machine? Well according to this reference "Across the MR industry, most scanners are 1.5T or 3.0T, however there are varying strengths below 1.5T and more recently, up to 7.0T.". They generate force enough to mechanically break components on a spacecraft.
At one hand, my reference for magnetic gradient is not so great, but you can search data for other orbital altitudes and redo the calculations yourself. Maybe one needs less thrust for higher orbit, but then the base magnetic field and its variations are also smaller.
But wait, there's more! (Trust me, I'm an Engineer). Strong magnetic fields especially if varying over time create electromagnetic interference which may mess up every wire onboard the spacecraft. Also, see this question for extended discussion. I'd even wager that a field this strong could mechanically damage the satellite by breaking its structure, I haven't done the math here, but I'm convinced by this video.
So, in summary: In orbit, and over the size of a satellite, and over the variations of the Earth's magnetic fields, magnetic forces (and not only torques) do exist all the time, but they are really small, to the point were any usable effect would require an insane amount of energy to generate an absurdly strong magnetic field which would probably destroy the satellite.
