In simple, conversational terms, the "null" hypothesis is an hypothesis that asserts that the cause of the phenomenon posited by the "alternative" hypothesis is NOT the alternative hypothesis. REJECTING the null hypothesis is equivalent to proving a falsehood. In the "real" (or statistical) world it is much easier to prove something FALSE than to prove it true (in the statistical world it is IMPOSSIBLE to prove anything of interest as TRUE). If the null hypothesis and alternative hypothesis are exhaustive and mutually exclusive, then proving the null hypothesis FALSE is equivalent to proving the althernative hypothesis TRUE.
Specifically, if one wanted to hypothesize that some geologic feature was a result of a "young" earth, he would have to demonstrate evidence to REJECT the hypothesis that the feature could result from an "old" earth. The earth is either YOUNG or OLD, and cannot be both or neither. To prove it is NOT old is equivalent to proving that it IS young.
This is where what you mention about C14 dating comes in: there is SO MUCH evidence for the "old" earth hypothesis, that any hypothesis that would be testable as a "young" earth hypothesis would probably have to contain within it "some" aspect that could overthrow almost ALL geologic evidences of an old earth, from centuries of study--VERY unlikely.
One hypothesis that COULD do that would be: god made lots of geologic features APPEAR to result from an "old" earth in order to test the faith of his human creatures. Problem is, such an hypothesis would itself be almost IMPOSSIBLE to demonstrate, because ITS null hypothesis would be almost impossible to reject: geologic features result from natural processes.
So, the fundamental null hypothesis required to be rejected, of ANY and ALL ID science, would have to be: The feature/process/trait under description arose from a natural process. Such a null hypothesis is VERY difficult to reject; unless, as I said, we found micro-etched serial numbers on animal structures--which, interestingly, is SIMILAR to the example often given in popular discussions of ID about writing in the sand being of "obvious" intelligent origin. You really would need evidence approximately that blatant to reject the ID null hypothesis that features of the natural world arose naturally.