Well Beth- that's a great question and I'm going to answer it but first, I want to tell you about Boxelder Bugs (I'm just "evil" that way)!!!
Scientific Name and Nomenclature: Order Hemiptera, Family Rhopalidae, Boxelder Bug, Boisea trivittata (Say)
An adult and nymph on a tree leaf (Note the link where I found this picture has several other good pictures of Boxelders and other insects if you are interested in looking at "bug" pictures).
Pest Status: Boxelder bugs are often considered a "nuisance" pest since they enter homes and/or buildings (particularlly stone ones) in search of winter hibernation areas. They can be vacummed up to be removed from buildings. Remember that I have said before that if you use the vacumme method you MUST remove the bag from teh vacumme and throw it out immediately. Insects can survive in harsh conditions and your vacumme bag with lint, food, and air is a very nice home for them where they can reproduce.
Host Plants (places where they can be found): Boxelder,
Caddo (Florida) Maple, Silver Maple (sometimes)
The life stages of the Boxelder bug
Overwinter as adults. Emerge in midspring, mate, and lay eggs. In the spring adults and nymphs will feed on seeds and maple trees. This first generation of nymphs may feed on dead insects including their siblings. These nymphs will emerge as adults in early summer.
In the summer and fall, the adults and numphs will suck sap from new tree (usually boxelder) growth and may feed on weeds and other plants. This type of plant feeding is usually non-damaging but when they feed on stawberries it can be very damaging. The second generation will occur in late summer and will have adult emergence in October. This generation is the one that will overwinter ater the first frost.
Whew!! Now I will answer the question
Yes, I think it's possible. Coccinellidae (Ladybug Family) beetles will feed on ANY arthropod that they can handle. So if there are lots of adults and nymphs around during the first or second generation of nymphs then it is likely that they will feed on them and consequently reduce the population. You can increase the number of ladybugs in your yard by making sure that you have plants that produce pollen, nectar, and honey dew for the adult insect to feed on. Another aspect to think about is what other beneficials (such as song birds, rodents, and/or other insects) do you have in your area.
Cranshaw, W. 2004. Garden Insects of North America: the Ultimate Guide to Backyard Bugs. Princeton University Press, Prenceton, New Jersey. Pgs. 230 and 544.
Pedigo, L.P., Rice, M. E. 2006. Entomology and Pest Management, 5th Ed. Upper Saddle River, New Jersey. Pg. 319.
Salsbury, G.A., White, S.C. 2000. Insects in Kansas. Kansas Department of Agriculture. Pg 100.