Yes, there is absolutely torques generated on the spacecraft from a combination of residual spacecraft magnetic field (static, produced by magnetic or paramagnetic materials in the construction) and dynamic resulting from the flow of electrical current around the spacecraft. There will be some interaction of these magnetic fields with the magnetic field of the magnetic torquers, however, that is typically minimal since the torquers generate much stronger fields. The individual torque sources, however, all add together in a vector sum.
On spacecraft where there is a desire to minimize these net disturbances on the control system, a magnetic balancing exercise may be conducted. During the design phase, use of magnetic materials are minimized. If they cannot be eliminated, subassemblies can be degaussed prior to integration. After integration, the residual spacecraft dipole can be measured then adjusted by adding trim magnets. This involves selecting a location which has minimal magnetic sources, measuring the location, then bringing the spacecraft to this area and spinning the spacecraft around to measure the effect on a stationary sensor to characterize the spacecraft dipole. This exercise can be done with the spacecraft in various power states to characterize the magnetic torque in the various basic modes of spacecraft operation. Note that solar arrays can be large contributors to the dipole as the loops the current flows through can be relatively large if careful attention is not paid to precisely how the backwiring is designed, so it may be critical to illuminate the panels and draw power from them for this test. Each principle axis of the spacecraft is measured by spinning the spacecraft around that axis. A vector sum can then be calculated and if desired, small permanent magnets may be epoxied to the spacecraft and the test rerun until the net magnetic dipole measurement is below the desired limit. A good description of a magnetic cleanliness program is found here: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710029225.pdf