If you are travelling through Germany the legal tread depth is 3mm, and yes they will fine you for anything less, and in some cases stop you from travelling further till you replace the tyre.
I just have to jump in on this thread because while I realise it's old it is unfortunately this is one of the top results when looking for A41 tread depth info.
This is false and I can only find this figure on forums. The legal limit throughout much of the EU and UK is 1.6mm, or 1.0mm where motorcycles have a specific regulation. Considering many mc tyres only come with 5mm tread to begin with, 3mm would be pretty ridiculous.
3mm possibly comes from outdated info or confusion about winter tyres, which have a higher limit.
Got to say I really like the A41, it's the only road biased adventure the I've used where the rear doesn't square off. The feedback from the tyre isn't massive but you get used to it. I'm going to fit a set to my Africa twin next
2850 miles on my 1250 GSA and rear about half worn and front still loads on. Just not certain what to do as in August going on 2850 mile European trip and bike will by then have around 3500 miles on current tyres before setting of on trip.