Solr index fields not showing a field
There is an apachesolr field collection module available, which makes me think that field collection support is probably not out of the box with the apachesolr stuff.

As a matter of fact, if you look at the issue queue for the apachesolr module you can find this ticket #1810228 : Process Field Collection Items. It confirms that field collections are not supported out of the box, and the comments point to the apachesolr field collection module, and indicate that the module may be buggy...

I'd say try it, but test your integration thouroughly. And do try both available versions (alpha and dev), and see how it goes.