NO.
Your flywheel sounds fine.
One side has a magnet and the other side a counterweight to balance the magnet.
If the magnet will pull a screwdriver in from about 1" away then it is fine.
However if the flywheel has been rubbing on the coil then the heat generated may very well have cooked the chip inside.
Unfortunatel there is no way of testing apart from substitution ( when you can do it with a hf signal generator & silly scope or a $ 40,000 test machine ) so take your old one to your friendly mum & pop mower repair shop and ask nicely if they can test it for you.