Evan,
Yes, if you bag you will definitely increase the likelihood that any seed set will be hybrid seed. However, if the two parents you are using are sufficiently and distinctly different, you should be able to tell just by looking at the progeny whether your cross worked or not. When I do crosses, I pick parents that are different enough, and for which the pollen parent is very different from the ovule parent. That way, if traits from the pollen parent show up in the progeny, I know the cross worked, whether I bagged or not.
LariAnn