hahahahaha thats a hilarious yet a very good idea!
First concern: When the robot gets over the edge, theres probably going to be an initial shock when the robots wheels leave the table from the robot falling until the tape is flat out on the table top. To lessen/rid yourself of this problem, just make sure the tape is being dispensed as low to the ground as possible(As level with the bottom of your wheels as possible).
Second concern: When the robot is repelling downwards, theres a good chance that it might begin to twist and turn. I think the only way to really compensate for that risk is to use either some very wide packing tape kind of stuff or use 2 strands of tape as far as possible away from each other
Third concern: When it gets near the bottom, its front is going to be facing the floor so your going to have to have some kind of wheels on its face so that it can drive forward just enough that when it cuts the tape it will fall down onto its bottom wheels instead of its face... or simply make it so the face is appropriately angled(like basically just make it a wedged front. The wedge is going to have to be up-side down ,so to speak, from what is the norm for that sort of thing so that when the bot lands, it rolls backward from the wedge so its wheels hit the floor rather than rolling forward onto its top plates) so that when the tape is cut, it cant just stand up on its face and start spinning its wheels.
Fourth concern: If a giant mechanical spider drops on my shoulder and scares the hell outta me I swear im going to beat you with a stick lol