Is each query batch in a dynamic SQL statement executed sequentially or can it be parallelized, when using sp_ExecuteSql?
Looking at the execution plan, you can see that every query is done as a different query. Again, if you want to see if those query are using parallelism, you will see it in the execution plan.

If each of the query can go parallel, then they will. 

Running this query agains StackOverFlow2013 DB:


  create table #tbl (tbl varchar(30));
  insert into #tbl values ('Comments'),('Comments')
  
  DECLARE @DynamicSql AS NVARCHAR(MAX) = ''
  
  DROP TABLE IF EXISTS #Results
  SELECT TOP 0 -1 AS DatabaseId, -1 AS ResultId, -1 AS ResultValue
  INTO #Results
  
  SELECT @DynamicSql = @DynamicSql +
  'select top 5000 * from [dbo].['+tbl+'] where text like ''%err%'''
  FROM #tbl t
  
  EXEC sp_ExecuteSql @DynamicSql 
  
  SELECT *FROM #Results
  
  drop table #Results
  drop table #tbl


you get an execution plan that does both select with parallelism.