That question has been fiercely debated in Britain, where Brexit day -- 29 March 2019 -- is depicted by some as the end of the world, and derided by others as a non-event.
Jacob Rees-Mogg, a Conservative MP and leader of the anti-EU European Reform Group, has famously complained that during this transition period the UK will be "a vassal state," deprived of any decision-making power in EU circles, though still stuck with the duties of a member state and still paying for the privilege.
Over in Brussels, however, that same question of what difference Brexit day makes is much less frequently voiced. Although Michel Barnier, the EU's lead negotiator, has repeatedly admonished his British counterpart David Davis that "the clock is ticking," the warning might equally be addressed to the EU27.
In just a year's time, British ministers will disappear from the European Council chambers where EU legislation is decided, and British MEPs from the committee rooms of the European Parliament.
Viewed through the distorting prism of the Brexit debate, this might be interpreted as a happy outcome for the remaining 27 nations of the EU: they will be free to go about their business without the burden of the UK's existential crisis (which has blighted its EU membership ever since 1973, some would argue).
But such an interpretation succumbs too easily to the calculus of the Brexit referendum campaign (and indeed the subsequent negotiations on the terms of exit) and its obsession with what the UK gets from its EU membership.
Much less talked about -- in Brussels as in Britain -- is what the EU gets from the UK's membership, beyond the much-disputed amount that the UK pays into the EU's budget.
What the EU gets -- and what the EU will be deprived of in just a year's time -- is a country that is a serious player on almost all fronts of EU policy.
It may not be the imperial super-power that it once was, but relative to most other EU states, it's still near the top. Most obviously, it's a serious economic player, with a particularly important financial services sector and its own currency. It's a serious foreign policy player -- a nuclear power with a permanent seat at the United Nations Security Council.
Less obvious, but very important to the EU, are the areas of expertise that flow from such strengths: in law and accountancy; in diplomacy and defense.
Those might be considered long-established traditional British strengths, but just as tellingly for the EU, the UK has been a pioneer in emerging areas of policy, such as information technology, energy and climate change. Some of that is a function of being a big and relatively open economy: companies will offer their services in the UK sooner than in, say, Belgium. But whatever the cause, the UK has developed experience and expertise that other EU states do not have.
Why does such expertise matter? Because what emerges from the EU's regulatory machinery is not always a simple arithmetical sum: the accumulated pros and cons of the 28 member states on a particular issue, nor even the lowest common denominator that all member states can accept. The process is subtler than that.
In both the Council and the Parliament -- and even in the European Commission -- the voices of the member states are listened to with varying degrees of attention. It matters whether you know what you are talking about, and whether you will genuinely be affected by the outcome. For that reason, the UK has had an arguably disproportionate influence on many areas of EU policy-making.
But that's not the only reason why there is so much truth in what has become a quiet refrain among British diplomats in Brussels: "You'll miss us when we're gone."
The UK will be missed also for the part it has played in supporting the states of Central and Eastern Europe.
In recent years, a succession of crises has hit the EU -- a credit crunch and bank failures threatened the eurozone membership of Greece, Cyprus and others, which in turn led to EU-imposed austerity programs. Waves of migration, some prompted by wars in Iraq and Syria, brought into question the Schengen area of border-free travel, and threatened the reign of Germany's Chancellor Angela Merkel.
Those crises tested the cohesion of the EU and called into question the loyalty of Western Europe to the 13 countries that joined in 2004 or after.
The Brexit negotiations have recently imposed an artificial unity on the 27 states that are on the opposite side of the table from the UK. But the East-West tensions remain, compounded by the anti-democratic antics of governments in Poland and Hungary; and discussions over the EU's next seven-year budget cycle will bring those tensions back into the open.
Moreover, Emmanuel Macron, the President of France, has ambitions to strengthen the powers of the eurozone (which does not include Poland, the Czech Republic, Hungary, Romania, Bulgaria and Croatia). Just as contentiously, he urges the EU to strengthen social protection and warns against unfair competition from cheap labor.
Broadly speaking, in such debates, the UK has been a counterweight to France and aligned with Eastern Europe: a liberal economy, championing competition, opposed to greater social costs and favoring a light regulatory touch.
The burning question in Brussels is who now, after Brexit, will be prepared to stand up to France? That question was put on hold while the German government coalition was being formed, and it is still too early to know the nature of the Macron-Merkel relationship.
Meanwhile, Italy's election seems unlikely to produce a government that will reverse the tradition that Rome underperforms in EU circles and Spain is distracted by the Catalan saga.
And still, the clock ticks down toward Brexit. Whisper it, but the EU is not ready for life without the UK.