How to include class features to linear SVM
The quick answer is yes, you can use a liner SVM in presence of an encoded categorical variable. 

Short explanation: The linearity of the model has nothing to do with the features of model, and actually linear feature doesn't mean anything. The linearity refers to the model, i.e. the equation that links the target to the features. 

The equation 

$$y = b*x + q$$

means that y is linear with respect to x, not that the variable x is linear. x is x thats it. 

What you should check when dealing with linear models is if your data is linearly separable, or in other words if you can separate the different classes with a straight line. If that is not the case you are in trouble and should probably think of changing the model.