No, nulls matter a great deal. If you want to test a claim in Null Hypothesis Statistical Testing, the "significance" of the claim is in direct reference to the null. Changing a null will change the significance of the alternative. My favorite statement of this is from Gelman:
> the p-value is a strongly nonlinear transformation of data that is interpretable only under the null hypothesis, yet the usual purpose of the p-value in practice is to reject the null. My criticism here is not merely semantic or a clever tongue-twister or a “howler” (as Deborah Mayo would say); it’s real. In settings where the null hypothesis is not a live option, the p-value does not map to anything relevant.
> the p-value is a strongly nonlinear transformation of data that is interpretable only under the null hypothesis, yet the usual purpose of the p-value in practice is to reject the null. My criticism here is not merely semantic or a clever tongue-twister or a “howler” (as Deborah Mayo would say); it’s real. In settings where the null hypothesis is not a live option, the p-value does not map to anything relevant.
https://statmodeling.stat.columbia.edu/2017/01/07/we-fiddle-...