Yes doing a CS along with LLB is one of the best choices of the combination of professional qualification one could pursue in this country.

ILS and GLC are both good and you'd benefit tremendously from both.

you can pursue Company Secretary and LLB Simultaneously. LLB is a three year regular course and CS is a distance learning course. So from this it is possible to do both at the same time but do remember since LLB is a regular course and It will restrict you from doing training of Company Secretary .

CS with LLB can be pursued professionally in a concurrent manner than CS with another profession.

In fact Organisation literally, hunt for those having CS as well as LLB qualifications.

So All the Best for the Career Endeavour.