That is far to few specs for anyone to answer except very generally... it's unlikely to work.
The 3s, 6s etc refers to the number of cells the battery has... The motor model you have will determine if it supports both 3s and/or 6s (11.1v-22.2v). Next you'd need to consider the amperage that motor will pull at the voltage you are using with a specific load ( the prop or rotor ) and if the batteries and ESC you have can support that load. Then you'd need to consider if the motor will spin fast enough... this is normally given in KV... the following is the definition for KV
KV as we use it refers to the rpm constant of a motor - it is the number of revolutions per minute that the motor will turn when 1V (one Volt) is applied with no load attached to the motor. In summary, we call it revs per volt
Typically a 3s motor will have a much higher KV than a 6s will... which would mean your rotor won't get up to speed but again, that is in general since you gave no real info other than the battery cell count.
Size and weight of the motor also factor into this since it'll need to fit the mount location and the aircraft must also be able to handle the weight of the motor... ie the heavier the motor, the more power it'll need to compensate and also affects the nimbleness of the aircraft.
If you want real answers for a technical question... you must provide the details or the answer can only be generalized and in the end doesn't give you an answer directly. You must provide what the exact make/model of motor and ESC are along with their specs when possible and then consider if the battery you plan to use can support the load you are going to ask of it.