p-value and conditional heteroskedasticity


conditional heteroskedasticity affects the standard error coefficient (in a t-test, multiple regression), but does not affect the coefficient of regression of the independant variable.

Does heteroskedasticity affect the p-value ?
Is it correct to compare the White-corrected t-test to the original p-value.... in order to decide about the significance of the t-test?

NB: by White-corrected t-test , I mean the use of White-corrected standard error (or heteroskedasticity-consistent standard error)

thank you