Yeah, it should increase by the same percentage. Informally, if you think of standard deviation as a measure of how spread out the data is, if you double the values, or whatever, they should become twice as spread out.
If each data point is multiplied by a positive constant, C, then the mean is multiplied by that same constant, C. Then when we compute the standard deviation by subtracting each data point from the mean and squaring it, we will be able to factor out a C^2: (Cx1-Cu)^2=(C(x1-u))^2=C^2(x1-u). This C^2 could then be factored out of all of the differences, and then when you take the square root at the end, sqrt(C^2)=C, so it would just be C times the original standard deviation.
Increasing something by a percentage is the same as multiplying by a constant, so it will work the same way.
