Mateo - no. Not in the automation mode being used. In other automation modes? Yes.
There are mistakes that can be made, like selecting 300 kts and a 250 heading vs 250 kts and a 300 degree heading. That occurred during a low altitude missed approach due to failure of the preceding aircraft to clear the runway. Simple manual flying while the PM fumbled with the automation inputs made it a non issue.
But the track of SIA 422 is not consistent with the mistake you mentioned. And VOR approaches aren’t flown in heading mode. If they were in heading mode, and switched the heading to 105(+/-) the turn would make sense. But there is no altitude setting of 1050 that would explain the mistake you mentioned.
And the missed approach altitude would have been set earlier and changing the heading selector, or changing the altitude selector, would not have changed the automation mode the aircraft was in.