Answer will depend on string. If your string is a Kevlar, polyester/co-poly that does not stretch, probably no. If your string is one that stretches, whether SG, Multi or co-poly, then perhaps yes. What you need at this point will be determined by your stringer and his/her machine. The amount of string required for the last mains and cross to reach the gripper varies a little based on how close the tension head can get to the frame. The amount of waste that a stringer can generate will depend on their experience. You should tell him/her your predicament to ensure they do not waste too much string at the end of the tie off main. May want to specify 1 piece so he/she DOES not cut the crosses off too short at the start of the string job. A machine does not guaranty stringer experience in all situations.
After all this, we still do not know what type of string you will be using. There are threads on your situation and many others including me have developed some common methods to ensure that we do not waste too much string.