No.

There is not a specific limit enforced on the number of rows in your database tables, nor the size of your database. 

At some point, your site will eventually hit a performance ceiling on its existing hardware footprint, and you may need to upgrade to a larger plan (i.e., more or bigger hardware) to accommodate your level of traffic, but we will do everything we can to help you keep your costs down — by helping you cache your site properly, optimize/reduce plugin usage, etc.

Primarily, database load has more to do with the types of queries you are running rather than the number of rows in your database.

Note: Our Shared vs. Dedicated Databases article talks more about what your Pagely database configuration might look like. Our standard plans use a shared RDS by default.