Not so far.

I've been going round in circles on the Globe's site, but have now discovered the locations and dates for The Merry Wives of Windsor: http://www.shakespearesglobeonscreen.com/merry-wives/ - mostly June 27th, but some early July dates. It's praiseworthy that many of the showings are in small or smallish towns (Ambleside, Boldon, Bury, Chichester, Greenhithe, Huntingdon, Newport IOW, Walsall, Yeovil ...).

If you then try the links from the MWW to the other plays, they all say "Coming Soon".

My nearest cinema is on the outskirts of Leeds. The one I'd be keenest to see would be Henry IV Part 2, but I'm dashing about quite a bit during July (London, Buxton, Stratford, etc.).

Incidentally, I'm currently reading James Shapiro's 1599, which has a lot of stuff about the (original) Globe. There's a lot of "Shakespeare may have ..." and "it is probable that Shakespeare ..." and suchlike, and there aren't any proper links to the immense bibliography at the end, but it's still a good read. I'd previously read his Contested Will in order to follow (and contribute a bit to) the goings-on at Wikipedia's article on the Shakespeare Authorship Question - a very good read.