I was recently convicted of a felony involving a firearm. Would that stop me from pursuing a career as an electrician?

No. Many people with felony convictions work in building trades. It might impact your ability to get a job with a particular contractor and I'm not sure if it will impact your ability to join a union. Some electricians work for themselves, and I would guess most people who might hire you would not ask about felony convictions. Working for yourself might be a good path to consider because it can be very difficult to get a job working for someone else with a felony on your record.