Think of that cover on the spark plug like a coil over plug on most cars. It’s a coil that bumps up voltage that is sent to the spark. That being said, it can be tested and there is a thread somewhere that has the primary and secondary resistance.
But before doing that, explain how you rebuilt the carb? A lot of times a carb that has old gas will need more than some spay and gaskets. I bought an ultrasonic cleaner a few years back and it does a great job of getting the tiny ports cleaned that are under the Welch plugs. Did you pop the Welch plugs and replace the diaphram
And clean out those ports? If it doesnt come up on full throttle it could be as simple as making sure the choke is off all the way, making sure the high jet is tuned properly, or something more complex like removing the Welch plugs and cleaning the hi jet port that goes directly in to the carb.
Hard starting can also be an issue with tuning on the low side.
id start with checking the carb stuff first before looking to replace the coil. First reason is they are very hard to come by. Second is when you find them, the seller knows they are hard to come by and they are not cheap.
Don’t give up on that saw. It’s my go to and surprisingly powerful for how old it is. I run a 28 inch bar on mine with a full slip chain and she pulls it very well. They don’t make high rpm’s but they just pull very hard
good luck
