Hosting Suspended with 1000+ Sites

Hi,

Recently, I got one of my hosting accounts suspended because one of my WP Multisite (with slightly over 1000+ members sites) causing CPU/mySQL overload ... exceeding the "fair usage" according to the (reputable) hosting company.

Now my question is, will this Multi-DB plugin solution eliminates such incident from happening?

My doubt is even if I created say the recommended 256 databases to share the load, aren't these mySQL databases still reside on the same server? Which means as per account, the loading will still be high to trigger suspension from shared hosting?

P.S. I'm crossing my fingers to avoid resolution being to upgrade to VPS or dedicated hosting.

Best Regards, William