Absolutely! You can quilt details into the applique shapes, or you can even do a cross-hatch design that goes right over the applique. Do what makes your heart sing!
Here is an example of stitching around the applique and adding cross-hatching in the background that I did on our very first TQS BOM in 2008:
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And here is an example of just stitching over the applique with cross-hatching, which was often done by hand quilters hundreds of years ago:
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Of course, there are hundreds of background fillers to choose from besides just cross-hatching, but I find that it's a classic motif and works well with most any applique because the straight lines offer a nice counterpoint to the curves of the applique shapes. For the same reason, I like to use curvy background fills on quilts that are mostly pieced with lots of straight elements.
If you will do a search on Pinterest for "background quilting" you will get lots of ideas!!
http://pinterest.com/search/pins/?q=background_quilting
Have fun!