Yes, it will be. The rate itself obviously depends on number of transactions and amount of data per transaction.. Both of those are specific to your implementation.

That said, as a reference, a Bitcoin transaction today is anywhere between ~160~1000 bytes, and the full block chain is on the order of tens of GBs. Is that a problem? It can be. To address this, Bitcoin uses Merkle trees and "Simple Payment Verification" (SPV) -- worth looking into, if you're interested.. long discussion on its own. I'll just note that SPV changes what you can say about integrity/security of the transaction.