Ask Mr. Smarty Plants

Mr. Smarty Plants understands that you want to grow Lonicera sempervirens (Coral honeysuckle) under a Prosopis glandulosa (Honey mesquite) and are concerned that the mesquite could possibly inhibit the growth of the honeysuckle.  Here's what I've learned:

1.  The leaf litter from the mesquite native to Central and South America, Prosopis juliflora (considered invasive in India and Africa) has been shown to be allelopathic to other plant species, inhibiting their growth.

In the paper, Community Impacts of Prosopis juliflora Invasion: Biogeogrphic and Congeneric Comparisons [PLoS One 2012 7(9): e44966] R. Kaur et al. report that the leaf litter of the invasive Venezuelan mesquite, Prosopis juliflora, has allelopathic properties that inhibit the growth of other plant species.

2.  The compounds reported to be the agents that inhibit growth in P. juliflora have also been found in extracts of the leaves of Prosopis glandulosa.

Hiroshi Nakano in the chapter "Plant Growth Inhibitors from Mesquite (Prosopis juliflora)" in the 2009 book, Desert Plants: Biology and Biotechnology, edited by K. G. Ramawat reports that his group has isolated the compounds (julifloridine, juliprosporine, julifloricine and juliflorinine) that are the bioactive inhibitors in P. juliflora and says that julifloricine and juliflorinine have also been found in extracts from the leaves of P. glandulosa. 

3.  Another book by R. Kourik, Designing and Maintaining Your Edible Landscape Naturally, says that the presence of P. glandulosa stunts tomato plants.

The evidence seems to indicate that there is the potential for P. glandulosa to inhibit the growth of the coral honeysuckle, but I don't think it is very strong.  I could find no studies that said outright that P. glandulosa was allelopathic—except for Kourik who says that it stunts tomato plants.