Could my coil be bad

ok i got new rubber caps that go in the carb next to the main jet, new needle and seat. Once again i cleaned the carbs to the best of my ability (i don't know much about carbs this is the first i've tried to rebuild). I put new carb holders on because small cracks were showing. choke on, pushed the button and started right up. My question is with the choke on (the only way the bike runs) does the air fuel mixture screws still apply? i did the three turns out and here is what happened. I had it in neutral reved it up and it would go up to four grand then bogg down before it would catch itself around a thousand. I thought finally after months of working on this bike i can ride it. go to take off and it misfired like crazy after giving it a little throttle. I decided to putt around anyway and after about ten minutes of giving it slight throttle, it came alive. I don't know what happened but it started running great. After about an hour of riding i noticed under throttle it ran awesome but when i was trying to maintain speed it would pop or backfire a little. Other than that i am so happy right now, this project has consumed me and finally i can ride it. I know i've been writing long stories but thought i'd share this experance. I might even ride in the rain tomorrow
 
When you say, it would only run with the choke on, that tells you that the carb is starving for fuel. The pilot circuit was/is partially blocked................mixture screw needs to be opened, pilot jet and passage ways.
 
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