No. In the case of true stalemate, then ID should not claim that irreducible complexity is proven and others should not claim that it is disproven. ID makes a lot of claims to have demonstrated things scientifically, but the “proofs” are often rather problematic. There is also the semantic question of whether “science does not explain this” is exactly scientific proof.
But the arguments to demonstrate irreducible complexity do not hold up well. As already noted, many complex structures in society developed gradually over time but now depend on many specific parts. Specific multistep biochemical systems can be observed evolving step by step in the lab.
Many of the Cambrian “priapulid” worms prove, on closer examination, to be intermediate, ancestral forms relative to the modern phyla Priapulida, Loricifera, and Kinorhyncha. Armored lobopods are intermediate between Onychophora and Arthropoda. Resources - BioLogos has a few articles relating to this, including The Cambrian “Explosion”, Transitional Forms, and the Tree of Life - Article - BioLogos The picture of the Cambrian diversification given in popular ID and young-earth sources is not accurate. There are varied Precambrian fossil animals; the Cambrian does not come out of nowhere. The Cambrian representatives of modern phyla are significantly different from and more primitive than later representatives, in addition to the many intermediate forms present. There are further myths that Walcott tried to hide the purported problems for evolution by tucking the fossils away in museum drawers. In reality, the fossils were reported not just in many technical publications but also National Geographic. The purported problems for evolution are that they appear relatively rapidly and that there are so many different kinds of organisms. But Walcott did not have any idea how long the Cambrian was, nor any good data on what was older. He did not recognize that the fossils did not all fit into previously known categories; the key techniques revealing details were developed beginning in the 1970’s.
The Cambrian diversification and Precambrian fossils have received extensive research over the past few decades, yet none of this work gets cited or acknowledged in claims about problems for evolution.
A more fundamental problem with the claims about irreducible complexity, specified complexity, etc. is that ID is painting a target around the arrow after it already hit the side of the barn. What is the probability of inventing an automobile? 100%. It happened. Given a planet with similar natural resources to Earth and a culture of organisms similar to Neolithic humans, what is the probability of an automobile being invented? Although it is quite unlikely that Thag would look at a lump of iron ore and a tar pit and think “I could build a ‘56 DeSoto!”, the chance of eventually building some sort of self-propelled wheeled transport is much higher. Similarly, the claim that a particular biochemical system is improbable neglects the question of how many possible biochemical systems could achieve a similar effect, or whether there are alternative systems that avoid the need for that particular effect.
The similarities between some of the tRNA genes suggests that the present system of protein assembly is built from simpler antecedents. Of course, there remains a sizeable gap between a simpler version of protein synthesis with fewer amino acids and less strict precision and abiogenesis. But the very fuzzy edges of that gap make it seem imprudent to claim that it could not possibly be spanned by further studies and discoveries.
The very choice of complexity as a focus is problematic. For information systems, the most complex things are random. The shape of a tree is much more complex than that of a lamppost. Simplicity is a better indicator of intelligent design than complexity when it comes to bureaucracy, paperwork, etc. ID seems to have looked for possible similarities between biochemical systems and human-made systems, rather than investigating what distinguishes designed and undesigned systems.
Of course, it is not possible to prove every single detail of what happened in the past. But the ID claims that evolution has gaps have not been of good quality. Nor is the theology good. God is at work in all that happens. Looking for random gaps in evolution is not good evidence for Christianity, or even proof of theism - the Raelian connections to ID highlight that. Expecting gaps in evolution also is in tension with the idea that God created all the natural laws so that the universe would work properly. Why didn’t He figure out evolution?