The answer to this one is almost always ‘no!’ The clue is in the name with no deposit poker bonuses, so don’t invoke your operator’s ire by trying to mess them about.
That said, poker is way more fun anyway, so it’s unlikely you’ll be tempted to commit bonus abuse, though some players do enjoy the occasional flutter for relaxation purposes so do watch out and make sure you’ve used up your poker bonus and met any required terms and conditions before playing anything else.
Alternatively simply use another site for your casino and sports betting – it’s easy enough to have two sites open simultaneously.