Is .NET Framework 3.5 still needed with a SQL Server 2017 installation to utilize Database Mail?
No, it is not required for SQL Server 2017.  The issue with Database Mail not working was fixed in 2016 SP1 CU2, and 2016 RTM CU2: 
FIX: SQL Server 2016 Database Mail does not work on a computer that does not have the .NET Framework 3.5 installed or stops working after applying SQL Server update

I know of several SQL Server 2016 and 2017 systems that are installed without .NET 3.51, and Database Mail is working fine.

Note that .NET Framework 3.5 was not included in Hardware and Software Requirements for Installing SQL Server, and that the SQL Server 2016 and SQL Server 2017 view of this page is the same.  The Database Mail issue was considered a defect in SQL Server 2016 and was fixed accordingly.