Cisco Switching/Routing :: 6500 Link Redundancy With Eigrp

Four 6500 connected to each other to form a full mesh.  Switches 4 and 7 is running eigrp.  A question came up, why didnt it have eigrp on SW 2 & 3 ?  Will it still be redundant if link between SW3 and SW4 is removed? If redundancy is working, SW3 should be able to find its way to SW4 via SW7 or SW2, yes?
 
The config looks:
 
SW4 eigrp
router eigrp 100
network 192.168.0.0
redistribute static
auto-summary
[Code]....

Recently, the eigrp was configured to SW 2 and SW 3 as well, it included the “redistribute static” statement. The route for SW2 and SW3 now has the VLANs, 51 or so. Sent ping from a PC to VLAN1 IP of SW3, then link between SW3 and SW4 was disconnected, network connectivity went down for about 20secs, and ping came right back. Thought it was a success. All of a sudden, outside connectivity was lost. Ping within the LAN was successful, but no internet connection.
 
The eigrp on SW2 and SW3 was removed, and the internet connection came back up. The initial concern was that although there is physical redundancy in place, the other routes may not be known. Hence, eigrp configuration has been attempted for SW2 and SW3. Perhaps the “redistribute static” should have never been configured on SW2 and SW3, SW7 does not have the “redistribute static” statement anyway.
 
Without eigrp running on SW2 and SW3, does it still have redundancy? For what it’s worth, SW4 and SW7 are both VTP servers. With the current configs, does it still have redundancy? Link redundancy was never tested; it always has been assumed that it works. Later today, with it’s current config, the link redundancy will be tested.