If on a diplomatic job,private plane to the steps or commercial to Vip lounge or whatever,if and when you give your details to the Military attaches office or embassy with your traveling party details and requirements,the team travelling are yours and known,on the other hand the drivers that are supplied externally from country to country are supplied to you from a so called trusted source and vetted by the attaches office of the country you are landing in,this is where it can be a can of worms as when you land and check out the people supplied you find all manner of things ,no licence/insurance /training,opposing none friendly country or religion etc ,these people all go airside including the drivers and their helpers on the baggage vans/trucks,this happens mostly in so called third world countries but with the influx of immigrant movements it has happened in all major airports in the world for many years ,its all down to the wage these people receive and the amount of middleman involvement.The US for a few years has had a decent system whereas if you have a party traveling by private plane more so if it of diplomatic nature all personnel traveling on the declared aircraft individually attend an interview at the US Embassy where papers/passport and background are vetted prior to travelling,the Military attache office for you also produce for departure and arrival the drivers details licence/id copies ,vehicle registrations/makes/colour etc which must tally on the days of travel for airside.It has been known in all major airports drivers do the pick up and when checked a short time later at the earliest convieniance its found that they have criminal convictions or are not of suitable type to have been airside let alone have licence etc.Obviously if you have the manpower and are in total personal control of the movement of your Royal or DP you would have sent an advance party to the country of intended travel to do all that is required of the advance team and all the vetting of the local workforce being employed for your party ,unfortunately in the so called third world the Attache/Embassies have the final say as they all want their backsheesh.In the past i have replaced criminals,illegal immigrants with no paperwork at all and on two occasions a wanted suspected murderer ,Awol from the legion ,French and Brit armed forces and even a supplied security/chauffeur driver for the principle who in his time had a conviction for drug smuggling (airside) and killing two people with a vehicle while working and losing his licence ,but was still working in a different country doing the same line of work.It is hard on you? you might not have the resources to send your number two chauffeur and PES driver on the advance to be waiting for you airside so you have to make the best you can do and using the team you have available.Everything is open to corruption and interpretation of the basic rules of security and easily worked around for the benefit of those requiring it,
So long story with simple answer, Yes you can have criminal convictions and get airside.This is my experience.