Can two switches talk to each other?

Yes, and you don’t even need a crossover cable for the connection on newer switches.

One important proviso is that this can be only on the default VLAN. If you use a different VLAN, the mode must be trunk rather than access.

C:\>ipconfig

FastEthernet0 Connection:(default port)

   Link-local IPv6 Address.........: FE80::260:2FFF:FE26:A3DE
   IP Address......................: 192.168.1.2
   Subnet Mask.....................: 255.255.255.0
   Default Gateway.................: 0.0.0.0

C:\>ping 192.168.1.3

Pinging 192.168.1.3 with 32 bytes of data:

Reply from 192.168.1.3: bytes=32 time<1ms TTL=128
Reply from 192.168.1.3: bytes=32 time<1ms TTL=128
Reply from 192.168.1.3: bytes=32 time<1ms TTL=128
Reply from 192.168.1.3: bytes=32 time<1ms TTL=128

Ping statistics for 192.168.1.3:
    Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
    Minimum = 0ms, Maximum = 0ms, Average = 0ms

C:\>tracert 192.168.1.3

Tracing route to 192.168.1.3 over a maximum of 30 hops: 

  1   0 ms      0 ms      0 ms      192.168.1.3

Trace complete.

C:\>arp -a
  Internet Address      Physical Address      Type
  192.168.1.3           00d0.9716.72ed        dynamic

C:\>