The short version is that legally it does get a choice, but it's probably up to the House of Commons to decide what it does.
The extension mechanism here is paragraph 3 of Article 50 of the Treaty on European Union (aka the Lisbon treaty)
- The Treaties shall cease to apply to the State in question from the date of entry into force of the withdrawal agreement or, failing that, two years after the notification referred to in paragraph 2, unless the European Council, in agreement with the Member State concerned, unanimously decides to extend this period.
As this makes fairly clear, the leaving member state (i.e. the UK) has to agree.
However, the EU Withdrawal (No.2) Act, (aka the Benn Act), the bit of UK legislation which is forcing this request also covers the response, so that If the EU proposes an alternative date than the one he's requesting (ie. the 31st January, which he must accept), then the Prime Minister must agree to it, unless MPs don't pass a motion (within two days of an EU decision) which approves the date suggested by the EU.