Yes, the person that wrote the counseling statement must sign the counseling statement.
While there is nothing in counseling doctrine that specifically states this it is common sense and it is also implied when reading counseling doctrine.
Think of it as a contract to be a legal document a signature is required. However keep in mind this could have simply been an administrative oversight. If the Counselor later discovers that they forgot to sign the form the fix is that they simply sign the form. The Issue is resolved!
If this is an event oriented counseling statement, in order for it to be a completed document it must have an assessment completed at some point in the future. A completed assessment is required for the form to be considered complete.
Previous Version of FM 6-22 Appendix B
FM 6.22 Appendix B, Figure B-11 (Still in effect until ATP 6.22-1 comes out sometime in 2014) states The assessment of the plan of action provides useful information for future follow-up counseling. This block should be completed prior to the start of a follow-up counseling session. During an event oriented counseling session, the counseling session is not complete until this block is completed.
Doctrine Update FM 6-22, ATP 6-22.1, ADP/ADRP 6-22
The doctrine list in the header above replaces FM 6-22 Appendix B, however it does not do away with the requirement to assess the status of the counseling session at some reasonable point in the future. If you attempt to separate a Soldier from service and you submit a counseling packet in which the assessments are blank a good defense attorney will argue that sense no assessment of the counseling was made the forms are incomplete.