Answer
No.
Work Step by Step
To have a current we must have a uniform surface charge distribution. This means that the charge density on the wire's surface will be constant along its length.
But in our situation, the electric field inside the wire is zero according to this charge distribution.
We can see that the given surface charge distribution is not possible because there is no net electric field inside of current-carrying wire.
In other words, the internal electric field in the current-carrying wire is zero, so that no current flows through the wire. Thus, the given surface charge distribution is not a possible surface charge distribution for a current-carrying wire.
