Did Shakespeare drink at Chaucer's Tabard Inn?

You probably know the Tabard Inn as the Southwark drinking establishment from whence Chaucer's pilgrims started their imaginary pilgrimage. The Tabard was a real place -- just off London Bridge on the south bank of the Thames, on the route from London to Kent and Canterbury, and it persisted (in one form or another) until the mid-19th century. And you probably know Southwark as the London suburb, on the south bank across the Thames from the City of London proper, that was home to Elizabethan London's riff-raff: prostitutes, bear-baiting, and commercial theatre.