Could stove element be powered through fan switch?
Original answer: no

Edit: Maybe

With the revised diagram and the path highlighted, the possible L1-heating element-L2 path via the fan switch is now discernible.  Theoretically, yes, you could have a heating element "shorted" through the fan switch.

However...

Cooktop switches (especially ca. 1983) aren't on-off switches, they are simmerstats - like slow, analog PWM controllers for resistive heating elements.  They function by drawing a small bit of current through a heating element inside the switch, which causes a bimetal strip to deflect and "pulses" the L2 contact.  A cursory Google search suggests the deflecting L2 contact is more likely to fail (open or closed) than for the relatively static L1 contact (held in place by the knob itself).

Therefore...

Your concern is at least somewhat validated because there is the potential for a short there (barring any fuses or fail-safe devices that aren't shown in the diagram).  However, since the L2 contact is left alone in your scenario, you should still be able to turn the burner off and control it normally, even if the L1 contact fails open.  It also seems as though the more common problem is a failed switch in general, resulting in a burner that either can't be turned on (relatively safe) or can't be turned off (decidedly unsafe).

Also...

Your primary concern is the voltage rating on the switch, which is rated at 6A @ 125VAC or 3A @ 250VAC (or 1/4HP @ 125-250VAC), but in the scenario you describe could see as much as 10A @ 250VAC.  Given that the switch is rated for motor loads, it is designed to handle high-inrush current levels at the moment the switch is closed.  So how well it fares in your scenario may depend on whether or not the fan was already running.  Given the unlikely nature of the scenario, it's plausible the engineers designing your stove weren't concerned about the possibility of powering a stove element through the switch in the event of an abnormal switch failure mode.