You can learn on whatever you want.
There are some places (in Ibiza and London, mainly) that do not allow controllers or laptops, but you can use USB sticks on their Nexus CDJ2000s (which do have sync). I think they have this rule to cut down clutter in the DJ booth and during changeovers as they usually have 1 DJ every hour.
There are also places in London which are vinyl only parties. Sounds great, but I have no wish to add to my 3000+ vinyl collection as I just have no more space and don’t wish to punish my back carrying them around anymore… if you are the same you won’t be playing at these places. In Spain, it seems normal to use controllers. I’ve used controllers when playing at Es Paradis and Eden (both Ibiza super clubs) with no problems, and a friend used his Traktor S2 when playing with me at Eden. I’ve seen many in big clubs use Traktor X1, or Traktor/Serato Scratch.
Basically, if you can beat match by ear, you can transfer your controller skills to using CDJs easily and to vinyl too, though you will need to label your records with BPMs to make things easier.