I'm not judging the merits of a cooperation. And Careful there, the Royal Netherlands Army and the German Army aren't one, they have a deep cooperation but they are both under the sovereign powers of two different countries.
In case Germany and the Netherlands go to war, yes. Otherwise, the integration runs really deep already. And that is pretty much what is supposed to happen with an EU army as well: withdraw in case you really want to, share capabilities in every other case. Just logical.
Let's have a look at the current military capabilities of the EU (without the UK)
Navy: 1 Fleet carrier, 3 STOVL carriers, 3 helicopter carriers, 17 amphibious assault ships, 31 destroyers, 74 frigates, 35 corvettes, 4 nuclear missile submarines and 48 attack submarines (nuclear and diesel-electric).
Landforces: 7000 MBT's, 12.000 armoured fighting vehicles, 8700 artillery pieces, 620 attack helicopters.
Airforce: 1300 Generation 4+ Jet fighters, 300-500 Generation 3 fighters depending on how you count and availability. 20 air refuel tankers, 300-400 medium sized tactical transport aircraft.
Total expenditure: 160 billion €, third in the world, roughly 200% more than Russia.
Active personal: 1.3 million people.
So, what do we get for all that money?
Around as much as Russia, MUCH less than China. Yes, certain things, especially personal costs, are more expensive in Europe which explains some of the differences. But most of it can be explained by single countries not being able to maintain larger equipment at all or in sufficient numbers, resulting in them either not having said equipment, having outdated versions of it, or having insufficient numbers to use it properly (most prominently when it comes to aricraft carriers, as having only one means you won't have any half of the time). The EU completely lacks large scale tactical transport aircraft, the largest being the Hercules and some old Antonovs at this point. Smaller airforces either keep older aircrafts for too long or are buying inferior material like the Gripen because of a lack of money. We don't have sufficient aerial bombardment capabilities. We have far too many frigates, because these are the largest ships most countries can afford, while lacking air support in form of carriers and AEGIS-like destroyer capabilities. We support an absurd amount of artillery pieces without having any real use for them on that scale.
In an ideal world, we would cut down on the number of fighter aircraft overall, while improving their quality and developing some bombardment capabilities. We would increase our number of MBT's while cutting costs though homologation. We would invest in large scale tactical transport capabilities and a larger number of attack helicopters. Germany and France would both invest in a fleet carrier, so that one will always be available, while other countries may pay for the airwings used on them.
All of this would vastely increase our potential while probably even shrinking the costs. It's a good idea.
