Red Ice on conventional control aircraft (cables & hyd actuators) I would most definately stop and not attempt to get airborn with the trim wheel. Consider the chances you have of servival running off the end of the runway campared to getting airborn and attempting to fly the thing on the trim wheel alone. If you have control lockes on your rudder would be locked as well so your looking at pitch control through trim and bank through differential thrust. As m&v said "stuff nightmares are made of".
On fly-by-wire aircraft the sidesticks are totally independent although interconnected. We have a training procedure of one sidestick failure after V1 and the procedure there is to immediatelly hand over control to the other guy/gall who will rotate the A/C and get airborn.