If it did cure allergies 10 times out of 10, and that ALL other possible cure-causes had been eliminated as causal beforehand (including the placebo effect which is inherent to most acts of taking a homoeopathic pill, even when the patient doesn't believe it'll work, simply out of subconscious memory of being cured by taking a pill), then yes, the posterior belief in its effectiveness would shoot up.

However, "the body curing itself by wanting to and being willing to even try things we know probably won't work based on what-ifs alone" is itself a major factor, one that has also been documented.

Par contre, if it did work 10 times out of 10, then I almost definitely would take it again, since it has now been shown to be, at worst, statistically correlated with whatever actually does cure me of my symptoms, whether that's the homoeopathic treatment or not. While doing that, I would keep attempting to rationally identify the proper causal links between events.