No - as Joe C points out, the regional and constituency ballots are now on separate pieces of paper making it impossible to pair up the ballots at the count. Indeed, the Electoral Commission's "easy guide" to the count states that the ballots are separated by contest before counting:
Depending on the space available at the count centre, ballot boxes for
both the constituency and regional contests might be opened at the
same time, or the CRO may open the ballot boxes for one contest first
and then open the ballot boxes for the other contest.
Ballot boxes are opened and emptied onto tables. The empty boxes are
shown to everyone present.
Count teams will check that there are no constituency ballot papers
mixed with regional ballot papers (and vice versa).
However, this was not always the case. In the 2007 Scottish Parliament elections, the ballots were combined onto one piece of paper, as below. The wording of this ballot paper caused significant confusion among voters, as many took the wording 'You have two votes' to mean that they could use both of their votes on one ballot, leading some constituencies to have over 10% of votes rejected. In some cases, the number of rejected votes exceeded the successful candidate's majority.
In the aftermath of this election, the Electoral Commission produced a review of the election to examine how this could be improved upon next election. Table 1.2 of Appendix D of the report shows a cross-table classifying ballots based on whether their regional or constituency votes were valid or not. It shows that 81,357 ballots had only their constituency vote counted, and 56,934 had only their regional vote counted - so even with the combined ballot paper, the votes were treated separately and voters were not required to vote in both the regional and constituency vote.