I see some theoretical potential that the general virulence of a bug (virus, bacterium..) to the human host could be (negatively) correlated to the immune-response caused by diverse vaccination methods against same bug.
While the ability of a bug to evade the hosts immune system e.g. by minimizing easily recognizable epitopes could establish a logical connection to the hosts immune reaction against vaccines presenting same epitopes, vaccine adjuvants diminish the correlation.
However, practically the bugs evolution against antibody recognition aims at preventing neutralization, while the prevention of immune-system activation is achieved via other mechanisms:
A common bacterial strategy, which is entirely uncorrelated to vaccination responses, is to produce proteins (virulence factors) that bind host antibodies to inhibit the host's immune system defenses. Another example that indicates poor correlation is production of virus-induced anti-inflammatory cytokines that may suppress T cell outgrowth.
Such suppressed cytokines include: Interleukin 10 (IL-10) or transforming growth factor β (TGF-β), or reduced production of inflammatory cytokines, such as IL-12 (Marshall, Urban, Welsh; 2011).
However, you seem to approach this question from a different standpoint:
For example, if someone had a strong reaction to a vaccine, this
person would also have had a severe course of the disease.
Here, you you seem to define the correlation as a function of different people as opposed to different bugs, while assuming constant vaccines and other factors.
Also, you define the "reaction to a disease" as the severity of the course of the disease. In contrast, the vaccination response quite unambiguously must be interpreted as the immune response.
As a persons good immune response against a vaccine should be correlated with a good immune response against the bug itself (independent events; no temporal order) and a good immune response against a bug (necessarily) has to negatively correlate with severity of caused diseases (as you passively define all other factors to be constant), the severity of disease should theoretically be negatively correlated with immune response to the vaccine. This also assumes that the recognized epitope(s) of the vaccine, that define the "vaccination response" are the same that define the immune response against the bug. Also, please mind that existence of a negative correlation per se does not state degree of variance coverage (compared to other factors).