No nor does it have logistical capability to deliver even half of the equipment currently being promised/discussed within a time-frame of less then 5-10year.
It's all dependent on the national government voluntarily following the advice of Brussels, and in most cases they don't really have the resources the EU wants them to commit to "The Ukrainian nationalist Cause".
EU has enough logistical capacity, but Russian nationalists like to dismiss EU like some kind of temporary group while they are riding donkeys to battle.
Lets talk numbers, rather then just sling cheap unfounded allegations
The problem with the way they talk at the big conferences is that there is almost no link between the rhetoric of existential crisis and the bills being passed at the national level.
The last numbers from Ukraine was a army of maybe 900k uniformed troops(thats up there with America) and as a response to that army's failure to drive Russia back Germany is talking about raising their armed forces less then a 3rd of that by 2030 thats just not real mobilization and thats my point about not taking the logistics serious.
Were the EU to mobilize as if it mattered to the actual population of the EU it could raise several time the army Ukraine have but nobody is actually suggesting that because the people in charge of the actual policy making don't really believe that Russia is a threat to any of the NATO member states.
It's all dependent on the national government voluntarily following the advice of Brussels, and in most cases they don't really have the resources the EU wants them to commit to "The Ukrainian nationalist Cause".