I am not aware of any evidence that roots release auxins, but I do know that microorganisms in the rhiosphere may release auxins, and affect plant growth.
Signal molecules like auxin,ethylene, cytokinin, LCOs, uridine and etc. are know to be involved in rhizobia interaction with host plants.
But, presence of Auxin concentration in the plant root is various depend on the environmental conditions and as well as requirement of host plant. So, it dependable.
Coleoptile region act as the cap for new root tip, which protect from the microbial infection. how coleoptile will act for this condition or interaction is I am not sure.
Plants use auxin as signalling molecule for symbiotic association, claim that some bacteria involve in producing IAA which act against plant pathogens directly and protect the host plant.
Few research articles are available regarding this, which gave evidences for your question.
Not only legumes, Also some other family members also posses symbiotic association which may or maybe attracted by hormones secreted by plants. One thing is bacterial colonies which require host for its life cycle, definitely it associate with plants. Either plant invite them by signalling or bacteria find its way by some channels.. Later it may be utilize by plant in positive way. Most of the medicinal plant do have association with microbes which directly or indirectly makes plants to produce chemical substance which have high value.
The plant hormone auxin is secreted in root apices via phospholipase Dζ2 (PLDζ2) activity which produces specific population of phosphatidic acid that stimulates secretion of vesicles enriched with auxin. These vesicles were reported to be localized at plant synapses which are active in auxin secretion, especially at the transition zone of the root apex. There are several implications of this vesicular secretion of auxin. In root apices, auxin emerges as plant neurotransmitter-like signal molecule which coordinates activities of adjacent cells via electric and chemical signaling. Putative quantal release of auxin after electrical stimulation, if confirmed, would be part of neuronal communication between plant cells. As auxin transport across plant synapses is tightly linked with integrated sensory perception of environment, especially of omnipresent gravity and light, this process is proposed to mediate the plant perception of environment. These neuronal features allow sessile plants to integrate multitude of sensory signals into the adaptive behavior of whole plants and the animal-like exploratory behavior of growing roots.Source :Plant Signal Behav. 2008 Apr; 3(4): 254–256.v