Support will be given for Linux software developed and released by the LSDev. As that time draws nearer there will be more information posted.
It seems there may already be a need for Linux support in general in SIL. A discussion took place at CTC 2006 in which this topic was discussed. A couple of documents were formed from that discussion, one which just gave the things that were discussed and another one with some proposal for what was needed for Linux support to happen in SIL.
The document about the discussion can be found here: Linux Support Discussion.
The document with some ideas and proposals is here: Linux Support Proposal.