Yes, if the regeneration depends on your preference of the generated words, the words order or link between them. The individual generations independent from each other, so if your choice – how many regeneration you do - not depends on the generations outcome, for example on your birthday date or favorite number, their randomness are equal.
But randomness are not enough, it's possible the first generated version correlate with your preference and that situation does not really matter why are you stopped generating new password.
Predictability of this scheme very good, because the strict rules. All implementation using common english words. For words smaller length, easy spelling, less ambiguity are preferred. Mixing nouns verbs and adjectives are more meaningful, order also adds more meaning. Word count very limited. Preference on the separator character also very rigid. Personal preference more known, because hidding your preference on all english words very hard and mostly unconscious.
On the other hand, I'd wager that the set of words that you can recognize is vastly larger than the set of words that you're likely to come up with on the spot. Hence, using a generator would still result in higher entropy then trying to come up with a password yourself.
Random numbers picked by humans are notoriously biased. I'm guessing it's even worse when you ask them to come up with random words.
But randomness are not enough, it's possible the first generated version correlate with your preference and that situation does not really matter why are you stopped generating new password.
Predictability of this scheme very good, because the strict rules. All implementation using common english words. For words smaller length, easy spelling, less ambiguity are preferred. Mixing nouns verbs and adjectives are more meaningful, order also adds more meaning. Word count very limited. Preference on the separator character also very rigid. Personal preference more known, because hidding your preference on all english words very hard and mostly unconscious.