The principles could be relevant (although I haven't verified (or read an independent review of) the proofs).
However, at least the execution is dubious: not only was a major cryptographic vulnerability found a few months ago[0], it highlighted that
1. they made their own unproven crypto hash, which is a red flag, (in production, you should always prefer crypto that has survived many years of cryptanalysis) and
2. they were really not up-to-date on cryptanalysis techniques, as being vulnerable to differential cryptanalysis is, as Bruce Schneier puts it, "a rookie mistake".
Worse than that, they seem to rely on security through obscurity, purposefully making it hard to analyse their systems by making it base 3 (instead of the obvious base 2 that all of practical computer science relies on).
Finally, their justification for the coordinator is also a red flag[1].
[0] https://medium.com/@neha/cryptographic-vulnerabilities-in-io...
[1] https://medium.com/@ercwl/iota-is-centralized-6289246e7b4d