From Microsoft Technet:
a Service Set Identifier (SSID), also known as the wireless network
name, identifies the wireless network. The SSID is a name configured
on the wireless AP (for infrastructure mode) or an initial wireless
client (for ad hoc mode) that identifies the wireless network. The
SSID is periodically advertised by the wireless AP or the initial
wireless client using a special 802.11 MAC management frame known as a
beacon frame
Looks like the SSID falls under Layer 2 (of the OSI model) which is the Data Link Layer.
EDIT: Layer 2 of the OSI falls under the Link Layer for the IP suite.
So the answer to your question is: Yes, the SSID for wireless routers are part of the link layer in the internet protocol suite.