Does alcohol-free beer contain any alcohol at all?

Usually a trace amount, yes - unless the can specifically says 0.0%. "Alcohol-free" as a UK label term covers anything up to 0.05% ABV, which most beers hit through the brewing and dealcoholisation process rather than by adding alcohol back in.

To put 0.05% in context: fruit juice, ripe bananas and bread can all naturally contain trace alcohol from fermentation at similar or higher levels. It is not enough to be absorbed meaningfully by your body or to intoxicate you.

If you need it to be genuinely, literally alcohol-free - for religious reasons, medical reasons, or just peace of mind - look specifically for "0.0%" on the can rather than relying on the words "alcohol-free," and see whether it is relevant to halal status or your own situation.