Do the shape and scale parameters have statistical interpretations?

Here is a Weibull proportional hazards model: $$h(t \mid \mathbf{x}) = h_0(t)\,\exp(\boldsymbol{\beta}^\top \mathbf{x}) = \gamma \lambda\, t^{\gamma - 1} \exp(\boldsymbol{\beta}^\top \mathbf{x})$$ Is statistical inference ever performed on the shape and scale parameters ( $\gamma, \lambda $ )? For example, do researchers ever comment on whether the estimates of the shape and scale parameters are statistically significant? Or what about determining the influence an extra unit change in shape or scale would have on hazard and survival rates (marginal effects)?