There are many ways to look at this:
Your Training
If visas are to be considered should you wish to save money by training abroad then the nation can essentially ask you whatever they want to. The United States, for example, may well want to look into your past with more scrutiny than a UK as they're not governed by our laws and reserve the right to do so. Further, the U.S. in particular conduct a search into your past above and beyond that for a visa should you wish to pilot an aircraft in their airspace. They're very anal following 9/11 and they have the right to be i guess. So, if they deem a drinking penalty inappropriate it could hinder you. If you are to train in the UK, the rehabilitation of offenders will apply.
Employment
If you're eventually employed in the UK post training then the role of pilot does not fall within the list of exemptions as per the "The Rehabilitation of Offenders Act 1974 (Exceptions) Order 1975" and therefore the employer can only ask about unspent convictions. When it comes to the UK CAA issuing an airside permit, the same applies and an explanation to that effect can be found on the UK CAA website. In this case it should work in your favour.
The drink driving conviction in the UK endorsed to a UK licence remains for 11 years from the point of conviction. If you're outside of this window you'll not have to declare it to an employer unless the role you apply to does fall within that exemptions legislation.
Hope that helps