Different types of chocolate additions at different times will yield different results. Some say to stay away from chocolates like that because of the fat content and preservatives. Fat can inhibit head retention and some say it can spoil your beer. I have heard of guys brewing with syrup, but most common is bakers chocolate in the boil or cocoa nibs in secondary(assuming there will be a secondary). I can’t confidently say you WILL be fine, but I’ve heard of folks using it and not having any issues. I just dumped 4 oz of cocoa nibs into secondary of an Irish coffee chocolate stout (Mocha Stout), but have never tried the syrup. I didn’t like the “fat” possibilities.
And yes, you will increase gravity by adding more sugar density to your wort.
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Here’s a good read: