The short answer is “no”. According to Apple’s blog post on the DMA, you’d have to be living in the EU for all of this to work and if you travel outside the EU, everything would continue working for a while and then stop. They didn’t specify after how long things would break, though.

To reflect the Digital Markets Act’s changes, users in the European Union are able to install alternative app marketplaces and install apps offered through alternative app marketplaces in iOS 17.4 or later. The country or region of your Apple ID must be set to one of the countries or regions of the European Union, and you must be physically located in the European Union.

Your device eligibility for alternative app marketplaces is determined by using on-device processing, with only an indicator of eligibility sent to Apple. To preserve your privacy, Apple does not collect your device’s location.

If you leave the European Union, you can continue to open and use apps that you previously installed from alternative app marketplaces. Alternative app marketplaces can continue updating those apps for up to 30 days after you leave the European Union, and you can continue using alternative app marketplaces to manage previously installed apps. However, you must be in the European Union to install alternative app marketplaces and new apps from alternative app marketplaces.

-Apple

Apparently it’s using GPS too so a VPN alone is insufficient? Didn’t find any YouTubers who’ve tried it.

Would it be possible to VPN to an EU address and download?

If so, I’d imagine things are going to get hard for VPNs not too long after.