Not quite. Again, εχοι is present, active, optative, 3rd person singular. That means the "it" is singular, and refers to τον λογον which is the object of the phrase above, speaking of the body of doctrine reasoned to them by Paul, out of which they chose ταυτα, (these things, predicate nominative plural neuter) to compare with The Scriptures, point by point.
Here is a translation that fits better:
". . . whether/if it (Paul's doctrine) might persistently/always/continually have these (things) thus (an adverb referring to the state of being 'according to and consistent with The Scriptures')."
The AV and the DRB versions using "those things" as the subject of the phrase, with the verb reflecting past tense in English, is really not quite a mistranslation--it is an interpretation that does not precisely render in English what is being said in the Greek.
Furthermore, to imply that every Berean accepted Paul's doctrine as "truth" to be believed cannot be so, for though many believed in his doctrine (that Jesus was/is Christ=Messiah), but for some it was not seen to be "truth," and thus did not believe.
What is true is that prior to their verification of Paul's doctrine as to authenticity in comparison to accepted inspired Scripture, they were open-minded and received his logos=doctrine (qualified in verse 2 above and in Heb. 6:1 as to its content) enthusiastically.
The issue of the truth of his doctrine is not the thought addressed here in this passage. It is the process by which the Bereans either accepted or rejected his doctrine that is in view, for all the Bereans used this process, whatever the individual outcomes were.
Accepting the doctrine by faith is the basis for accepting it as Scriptural truth as a continuation of God's progressive revelation of Spiritual truth, when it is compared with the body of already revealed, inspired truths in the law and in the prophets. This is the only valid method of fixing the apostles' doctrine as worthy of canonicity, not by holding that its fallible hearers and practitioners could be more authoritative than The Scripture Itself.
In summary, the words of uninspired translations like AV and DRB may be corrected, especially when they encourage inconsistencies in application. The words of the verbally inspired infallible Scripture may not be corrected, nor should translations yield to undermining the meaning of and in the context.
As an aside, the above passage firmly commends revealed Scripture as the ultimate authority in settling doctrinal disputes.
That may be all good and fair but none of that changed the intent of the passage. I don’t believe anyone said or left the impression that all the Bereans believed. The intent was as you said in your last paragraph. Scripture as the ultimate authority in settling doctrinal disputes and Paul was using them as an example of not falling for the teachings of false teachers.