Not necessarily. The regularization term will modify all parameters which are is its computation graph.
Have a look at this dummy example:
model = nn.Sequential(
    nn.Linear(1, 1, bias=False),
    nn.Sigmoid(),
    nn.Linear(1, 1, bias=False)
)

criterion = nn.MSELoss()
x = torch.randn(1, 1)
target = torch.ones(1, 1)

output = model(x)
loss = criterion(output, target)
loss.backward()

lin1_grad = model[0].weight.grad.clone()
lin2_grad = model[2].weight.grad.clone()
print('Before regularization')
print('Grad lin1: {}'.format(lin1_grad))
print('Grad lin2: {}'.format(lin2_grad))

# Add regularization to lin1
model.zero_grad()
output = model(x)
loss = criterion(output, target)
loss = loss + torch.norm(model[0].weight)
loss.backward()

lin1_grad_reg = model[0].weight.grad.clone()
lin2_grad_reg = model[2].weight.grad.clone()
print('After regularization')
print('Grad lin1: {}'.format(lin1_grad_reg))
print('Grad lin2: {}'.format(lin2_grad_reg))

As you can see, the gradient for lin2 stays the same, while the gradient for lin1 changes.
This is due to the fact, that the parameters of lin2 were not involved in creating the regularization term, so they won’t be touched.