It is worthwhile to note that the
NP cannot only be applied to polynomial problems: If
X is a particular set of problems that can be decided in a time bounded by a given characterisation (that is, polynomial for
P or exponential for
EXP) by a deterministic Turing Machine (DTM), then
NX will be the set of problems that can be decided by a non-deterministic Turing Machine (NTM).
So the question is how the FID truly works. Do you have to solve a problem that can be decided by a DTM in polynomial time every time you want to jump? If you built a machine that used the FID to remove the required non-determinism from the run of a TM, you would essentially have built an NTM. This actually makes sense, because although the problem space is (or rather might be) infinite, one particular instance of the problem is always finite. So the probability to always "guess" correctly is finite. In this sense, the FID would be the technological equivalent to the computation model of an NTM. So, in general, in a universe with an FID, there is no practical difference between any
X and its corresponding
NX class of problems, but it would still be unknown whether they are actually equal (as they are defined over TMs, not IDs).
However, it doesn't make sense to argue about the total runtime of an algorithm that crunches an infinite input, as in all but some trivial cases that would be infinite as well.
If IID is just some sort of mathematical problem, that once solved just hands you some insight to build a machine that implements some kind of propulsion, then the question is how hard is this problem? We have no indication whatsoever that it would fall in the class of
NP-complete problems. There are a ton of
NPSPACE) problems, and actually even some
NEXPTIME. If it was
magical advancedly technological FID would be no use to you, you'd wait just as long.
So, the relationship between any
NX would be like "fixed improbability drive" and "finite improbability drive". It'd seem the infinite improbability drive would rather correspond to a machine that decides every single problem in constant time, regardless of its complexity on a DTM or NTM because an infinitely improbable event is basically one that never happens. There are no such events thinkable: Even two nuclear warheads spontaneously transforming into a bowl of petunias and a very surprised looking sperm whale is not an impossible event. It is just so unlikely nobody bothers to put a warning sticker on such warheads.
To finally answer your question then; No, I don't think Adams would have done such a pop-science blunder. His wibbly-wobbly parts (in lack of a better term) are always intentional and work more in an ironic manner. The IID slightly reminds us of the non-determinism issue as it does something mind-bogglingly hard in a spectacularly efficient way, just as an NTM would. But this similarity is quite superficial, as I tried to point out in the previous paragraphs.