I think the solution may in theory help you increase the performance, but it also depends on what the scalar function actually does. I think that in this case (my guess is formatting the date to last day in the quarter) would really be negligible.
You may want to read this page with suggested workarounds:
Because SQL Server must execute each function on every row, using any function incurs a cursor like performance penalty.
And in Workarounds, there is a comment that
I had the same problem when I used scalar UDF in join column, the performance was horrible. After I replaced the UDF with temp table that contains the results of UDF and used it in join clause, the performance was order of magnitudes better. MS team should fix UDF's to be more reliable.
So it appears that yes, this may increase the performance.
Your solution is correct, but I would recommend considering an improvement of the SQL to use ELSE instead, it looks cleaner to me:
AND ReportTypeID = CASE WHEN (@X = 1) THEN 1
ELSE 4
END;