No.
It is the most sacred site in Ethiopia. One man lives on site 24/7 as its guardian.
IIRC, each of these guardians lives a short life marked by physical ills, cataracts, cancer and other illnesses associated with chronic radiation exposure.
In any event, as the most sacred site with the most sacred artifact in the country, it has an abundance of armed guards outside the holy ground.
Mostly the curious are firmly but very politely forbidden to enter (I've had an Ethiopian roommate, he could be quite polite and persuasive, I can see a whole country of such making is so a determined seeker would back down out of reciprocal politeness!)
No Christian or Jew, or probably Animist for that matter, would intrude.
A muslim might murder half the country to seize it, but I would advise them to consider the fate of Pompeii (the person, not the city) after he intruded into The Temple's Holiest of Holies.
There's a single guardian who keeps watch 24/7, and it's a great honor. They don't leave the shrine until death or shortly before that. They train their replacement, so, for a short while there are two living people who have seen the supposed Ark. If I had to guess, it would be that the purported Ark in Ethiopia is an Egyptian royal coffin of some sort, nothing to do with ancient Israel at all.