You can! With a bit of CellProfiler workarounds See the attached pipeline file, which works with your original image.
The trick is to use ReassignObjectNumbers, which has a per-parent convex hull option. To use this though, you need to identify child and parent objects. That is the use of the two IdentifyPrimaryObejct modules. They are exact duplicates of each other, except for their output objects’ names. Then you need to establish a parent-child relationship, but here, they are exactly the same objects as just stated. Then you can use ReassignObjectNumbers with the per-parent convex hull object. The MeasureObjectSizeShape is just there to verify that the convex hull objects are truly larger in area, etc. (I’ve never tried this otherwise, so please verify these measurements yourself!)
Hope that helps!
ConvexHull.cppipe (9.4 KB)
P.S. This was created with a recent nightly version of CellProfiler (http://cellprofiler.org/releases). But it doesn’t need to be. If you have an older version of CellProfiler, then it may work immediately, but if it complains on import, then you could download a new version and open it there, then manually create the pipeline in the older version with the same basic settings.