Let's see if the data bear that out. Going back 12 years (thank you, ESPN), here are our records in January and in February:
2013 -- Jan: 4-3; Feb: 5-3
2012 -- Jan: 2-5; Feb: 3-6
2011 -- Jan: 6-2; Feb: 4-4
2010 -- Jan: 4-5; Feb: 4-4
2009 -- Jan: 9-0; Feb: 7-1
2008 -- Jan: 6-3; Feb: 7-1
2007 -- Jan: 2-7; Feb: 4-4
2006 -- Jan: 8-1; Feb: 6-1
2005 -- Jan: 4-4; Feb: 7-1
2004 -- Jan: 7-2; Feb: 6-2
2003 -- Jan: 5-3; Feb: 5-3
2002 -- Jan: 8-2; Feb: 6-2*
*We played a lot better late Feb-March, so this is a little misleading
Over those 12 years, I count 3 years when I'd say we were demonstrably better after late January -- 2002, 2005, and 2008. Those were sophomore-led teams that grew up dramatically and went on to earn protected seeds.
More often than not, teams that were decent in January stayed decent in February but didn't dramatically improve (2003, 2011, 2013), teams that were dominant in January stayed dominant in February (2004, 2006, 2009), and teams that were lousy in January remained lousy in February (2007, 2010, 2012).
By and large, the "UConn always gets better in February" narrative is overblown, at least over the last decade. While we have looked a bit better of late, I wouldn't hold out for a drastic improvement from this extraordinarily veteran bunch.
Other items that jump out at me: (1) It's been almost 5 years since we had a truly UConn-caliber regular season where we dominated wire to wire (2009); those used to be frequent occurrences, but nothing close to that lately. (2) How in the hell did we manage to go 5-11 in January and February in 2012 and still be a lock for the NCAA Tournament come Selection Sunday? I had forgotten/didn't remember just how putrid that team was.