Boxing is definately a good thing to learn with your grappling base, especially for street situations. In terms of transferring to MMA it will help there will be alot to adapt to and somewhat unlearn. For example, we have a golden gloves champ at our gym. He hits f'in hard but can't deal with either getting or receiving kicks, not to mention grappling etc.
Ultimately, it depends on what your goal is. IMO, If you want to learn MMA, go to a MMA gym where you will learn everything (including boxing and other standup). Boxing is good to learn on its own and is a blast to learn.
On a side note, my base was grappling also and it took some time to getting used to hitting others and getting hit.