can QB handle a database of 250M records

That will depend on on the design of the whole app in terms of how many fields you will have in each record, how many relationships and summary fields you expect to have and if you will have many complicated formula fields.

If your 250K records have less than a dozen fields AND you are not making extensive use of relationships, yes!

One other idea.

CloudBase Services can integrate Quick Base with a SQL database on your server, Amazon or anywhere in between.  The other database can hold millions of records and Quick Base can "call on" the records to show your users any data they need.  Contact us via our website for more information.