Does Compressor 4 do this conversion? And is it possible for it to convert multiple files at once?
Yes and yes.
The 4S shoots h.264 Quick Time.
For FCE, you will need to convert to Apple Intermediate Codec.
For FCPX, you can edit the clips natively if you want. I haven't a lot with iPhone material, but when I have, it went smoothly. However, I typically create optimized media because I have plenty of storage and not concerned about files size.
You can drag multiple file into the Batch Window. Then drag the setting and destination of your choice to one of the panes and they'll all populate. If this is going to be a recurring workflow, you could also create a droplet. Once it's set up, it's the simplest way.