Only barely. It’s been a major hassle to get parliament approval for the Bundeswehr acting outside the country, even those are mostly supportive roles, not bombing and firing at people. And it’s not really popular at home. Balancing the deeply ingrained do-not-kill-provisions, human rights/dignity provisions in the Basic Law and Realpolitik and the requirements of our alliances is very tricky.
Article 87a)
(2) Außer zur Verteidigung dürfen die Streitkräfte nur eingesetzt werden, soweit dieses Grundgesetz es ausdrücklich zuläßt.
“Apart from defense the armed forces are only allowed to get deployed when the basic law explicitly grants permission.”
(Translations may sound clumsy, but I tried to pick words are closely in their meaning as possible.)
Foreign adventures were not among the permissible acts back when the Basic Law was drafted, but Germany loosened up the restrictions since the 1990s. But it’s a slow and ongoing process. The German armed forces are defensive by design and are badly equipped - including legal provisions and public acceptance - to operate outside out borders.
See 2009 Kunduz airstrike - Wikipedia for how the accidental, if not negligent/reckless killing of civilians in what is basically a war zone shakes up the government over here.
And the other part I already mentioned: If Germany would seriously beef up militarily, our allies and partners in the EU, would become nervous, especially Poland, where there are people who still expect us to come back and reclaim the territory ceded de facto around 1950 and de jure in 1992.
For Americans, World War 2 and German agreesion is a time told by veterans and, to some extent, people who fled from war and prosecution. For Europeans it’s a tale of mass victimization of civilians with regular reminders like huge rows of bunkers, mass graves and, of course, unexploded ordnance to be found when you dig deep enough. In Germany, the daily average of that is 15, most of them aerial bombs.
