No, but we've been running Java7 internally for quite a while now. Official certification/support is coming.
If you do run Java7, be sure to use SQL Developer v3.2.20_09 as we had critical bugs with earlier versions, particularly around scrolling in data grids - fetching additional results wasn't working.
With regard to the 3.2.x and lower releases, no, as those releases pre-date jdk1.7.0_13. For some comments on the usability of the latest production release, 3.2.20.09.87, with jdk1.7, see the following: Re: Java 6 EOL, Java 7 not certified
As for the next major release of SQL Developer, we'll have to wait for the announcement and associated release notes.
SQL Developer Team