For every airline I have had the pleasure of working for criminal record checks are conducted. For a airside pass you have to provide references for the last 5 years minimum.
I sold my business at 25 and did my training and it worked out for me but I know of several of my colleagues who are now bankrupt because of the loan repayments and low wages at some carriers. I am really sorry to say it but I honestly think in this climate you would struggle. If it were me I would at least wait until the conviction has lapsed because no company will entertain it in my opinion.
I mean this in the warmest sense