Yes, Serene Grace and Charge Beam do interact in this way. You would effectively have a 140% chance to trigger the Special Attack boost, which the mechanics of the game would simply cut to a 100% chance.
No, you really shouldn't do this with Meloetta. It might work sometimes, but you are losing a lot of offensive ability with Charge Beam due to it's relatively speaking low BP at only 50, not to mention it's accuracy is 90% meaning you will occasionally miss.
If you were playing a more mixed defensive set you could use Calm Mind in order to setup both your Special Attack and your Special Defense, given Meloetta-Aria's stats naturally working in this direction (losing the Electric type attack altogether, however). However, the set you are proposing would work better with Thunderbolt, or if on a Rain team, Thunder (no accuracy check in Rain). Serene Grace would raise the Paralysis chance to 20% and 60%, respectively.