Need some help identifying...

I have a '96 LSS and changed the O2 sensor today. When I did I notice a hose broke off. Not sure if I did it while changing the o2 sensor or its been like that. Not sure what the part is or what the hose does. The 1st pic is of the unit it broke off of and was connected on the other side to the firewall. 2nd pic of the hose. Looks like a plastic connector was melted.
http://i1110.photobucket.com/albums/h448/tcduhon/DSC06934.jpg
http://i1110.photobucket.com/albums/h448/tcduhon/DSC06935.jpg

That hose is supposed to connect between the blower motor and the fire wall. If you look/feel under and on the fan motor, you will find a hole, thats where the long section is supposed to attatch into the motor, there will be a fitting on the fire wall to attatch the smaller section to. It looks like it has been off of the motor for a while and melted by the exhaust. Will need a new one to get it to seat into the motor.

That hose is supposed to connect between the blower motor and the fire wall. If you look/feel under and on the fan motor, you will find a hole, thats where the long section is supposed to attatch into the motor, there will be a fitting on the fire wall to attatch the smaller section to. It looks like it has been off of the motor for a while and melted by the exhaust. Will need a new one to get it to seat into the motor.
What does this hose do? My A/C seems to work fine????

It allows air back to the blower motor to help cool it.

Is it bad if I drive around without this hose on?

The tube allows cooled air from the a/c to cool the blower motor. Without it, you can expect the motor to have a shorter life span. HVAC operation will not be affected though, until the motor quits.