Well, it seems they did: the Lochside Leisure Centre in Forfar.
Staff there were amazed when the couple turned up at the municipal complex to play five-a-side football.
They were understood to be spending the New Year in the Angus area.
Unsuspecting workers at the leisure centre had a booking in the name of David Ogilvy, the 13th Earl of Airlie, for a five-a-side court on the afternoon of December 31.
The Earl maintains two homes on a 60,000 acre estate near Forfar – Airlie Castle and Cortachy Castle.
But workers at the site were astounded when Tim Burton – famed for directing movies such as Edward Scissorhands and Alice in Wonderland – and Helena Bonham Carter, who played Bellatrix Lestrange in the Harry Potter movies, turned up to take part.
The centre's staff later snapped a picture of the couple and posted it on Angus Leisure's Facebook page.
One worker, writing on the page, said: "They just came in to play fives.
"The booking was under David Ogilvy from Airlie Castle so I think they are just here to bring in the New Year."
A council source said: "It was a massive surprise for everyone at the centre – they're not our usual customers anyway.
"They were really lovely – a great couple and very down to earth and they seemed to enjoy their visit.
"They will, of course, be welcome back any time."
Tim Burton and Helena Bonham Carter began their relationship while filming Planet of the Apes in 2001.
They had their first son Billy in 2003 and their second, Neil, in 2007.
Carter is regularly cast in Burton's films – though she is best known for her appearances as Bellatrix Lestrange in the Harry Potter series and as Queen Elizabeth in The King's Speech, which saw her nominated for several major awards.