Is a German Surfstick usable in other EU countries?

I'm flying to Gran Canaria soon and have no Wi-Fi in the apartment. Now my question: Would it work, if I have a surf stick here with me? 10 GB of data, and then put it there in the laptop and surf on mobile data?

After all, there's only one SIM card in the surfstick, as in the mobile phone… And since June 2017, my mobile data on the mobile phone also work well in other EU countries. So why should not that work with a SIM card in Surfstick too? Or am I making a mistake here?

The tariff is according to your simcard. In the EU-Auslands then the same costs apply as in Germany. Only if the agreed data volume is exceeded can additional costs of approx. 3 cents per MB be incurred.