I disagree with both answers. That is, I feel that the rules do adequately answer the question, and do turn the attack into a critical hit.
There are two scenarios of interest: the actual target AC, taking into account the attacker's attack bonus, requires a die roll of at least 20, or it requires something higher than 20. Let's consider the latter case first. In that scenario, the only way to hit is to apply the rule under "Rolling 1 or 20". Let's also assume that Convergent Future allows success in every possible scenario (which seems to be the intent). Then…
From PHB 194:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target's AC. In addition, the attack is a critical hit, as explained later in this chapter.
The description of Convergent Future specifies that the player can "ignore the die roll and decide whether the number rolled is the minimum needed to succeed".
Now, admittedly this is a difficult sentence to parse. It first says you ignore the die roll, and then says you decide whether that very die roll is the minimum number to succeed.
One way to interpret that is that they don't actually mean you ignore the die roll, but rather you get to selectively adjust the target number (i.e. AC) so that it temporarily equals what you rolled. That would be consistent with "decide whether the number rolled is the minimum needed".
But that's clearly in conflict with the idea that the die roll is ignored. You can't ignore the result and then say that the result does apply and you're just changing the target value for success.
Another way to interpret the sentence is that by "decide whether the number rolled is the minimum", they mean that rather than the number shown on the die itself, you select a different number as "the number rolled", one that is equal to the minimum required for success. I find that this interpretation is much more sensible, requiring a lot less in the way of linguistic contortion to justify. The sentence structure is awkward, but the intent seems clear to me.
Okay, so having established that you are in fact changing what's rolled, now we look at the rule for critical hit. The only way to apply the rule to successfully hit at all is to assume that the "Rolling 1 or 20" paragraph applies. If it applies, then necessarily it must be the case that "the d20 roll for an attack is 20". There is no other rule that would allow for a hit in this scenario, and so we must be applying that paragraph. If we are not, then there is no way for Convergent Future to result in success, but we took as a given that it always can.
Since we are applying that paragraph, then there's no reason to think that the whole paragraph does not apply. So the second sentence must also apply, meaning that when the die roll was taken to be a 20, that necessarily means it's a critical hit as well.
Okay, so what about the scenario where the AC required at least a 20. In that case, the rules do allow for success even without the language under "Rolling 1 or 20". It can be treated as a normal hit, based on the actual die roll meeting the target number required.
Suppose we say that in this case, it's not a critical hit. Well, technically that'd be fine according to the rules as written. Except that we've already determined that if the AC requires a die roll higher than 20, you still hit and it's a critical.
I don't think it makes sense that you can't have a critical hit result with the AC at exactly 20 plus the attacker's bonus, but can when it's higher. If you could, that would mean that higher AC is actually more dangerous for the target for an identical attack roll. That seems illogical to me, and so I find it contradictory with the IMHO logically sound conclusion of the other scenario.
So for logical consistency, it must also be the case that if AC requires a die roll of 20, Convergent Future also results in a critical hit.
That covers both scenarios, and in both cases you wind up with a critical hit.
Now, all that said: the above all relies on the assumption that Convergent Future is intended to always guarantee success. If you don't take that as a given, then the conclusion could be the opposite: Convergent Future doesn't actually change the roll as used in "Rolling 1 or 20", and so that part of the rules would never apply. Only by actually rolling a 20 could one hit a target with AC higher than 20 plus the attacker's bonus, and even for targets with AC of exactly 20 plus the attacker's bonus, Convergent Future can only give you a hit, not a critical hit.
I don't personally think that's the right way to interpret Convergent Future, but I would have to admit that if someone chose to do so, it would change the analysis above.