Not an expert but as its a criminal conviction I would think you wouldn't have to worry about an airside pass as you may not have a job to worry about. On the form in the section on criminal records that aint going to go down well.
Not sure what the rules are for how long until a conviction is spent. However the spent conviction scheme doesn't apply to certain criteria ie jobs of a sensitive nature so even if you eventually got a job an airside pass may fall into this category.