Is a DSL splitter required, if only a Modem is attached to the line?

A DSL filter performs 2 functions:

1. To prevent DSL frequencies from reaching non-DSL devices

2. To prevent spurious noise from non-DSL devices from interfering with DSL frequencies

If there are no non-DSL devices on the line then no filter is required.

Reference ADSL Filters & Splitters

You should use a filter anyway. The filter performs two main functions:

1. Prevents the ADSL signal interfering with the voice part of your phone line (not required in your case as you have no phone connected)

2. Ensures that the ADSL line is terminated correctly. An unmatched termination may cause reflections back down the line. This can cause errors on the ADSL connection.