just check something first...

trace/follow each of your relay wires and see where they go.

if the positive from coil is high current draw then it will probably affect your coil. I wouldn't put 2 high load items on one circuit.

if however, your fan switches on when your coil is active it means this is likely to be your low current switch. You can check by following the relay wires to see where the other power is obtained from... lazy sparkies will piggy back to anywhere but a good one will have taken a nice robust source like your alt, starter post or a big fat cable.

If it turns out it is on your switching circuit, I would leave it with no detrimental effect to coil operation.

sorry if I'm confusing the issue.

summary: first step, work out if this is your low or high current circuit attached to coil.

Cheers
Ed