This is a question which is getting somewhat close to opinion, since it requires soothsaying an alternative future, based on events which did not happen, but in terms of evidence:
The victory in R (Miller) v Secretary of State for Exiting the European Union only directly caused the passage of the European Union (Notification of Withdrawal) Act, which in its enacted form did not contain any provision for meaningful votes, but did place the term in the media during its passage through the House of Lords.
A "meaningful" vote became statue in the European Union (Withdrawal) Act 2018, which in section 13 required parliamentary approval of the withdrawal agreement and future relationship. Since this act also repeals the European Communities Act 1972 (i.e. the basis for UK law tracking EU law) it or something like it would very likely have needed to be passed, regardless.
So the question comes down to "without R (Miller) v Secretary of State for Exiting the European Union", would anti-hard Brexit feeling have been strong enough to make Parliament introduce a check on the Conservative minority government?". I lean to "yes", but an alternative history novel in which they didn't isn't totally out of this world.