1GB is quite large, you won’t get there too quickly. Furthermore, there’s plenty of cheap hosting plans out there with unlimited db size.
Doing what you want is in theory possible by hooking into the query and a whole bunch of other filters, but it’s pretty complex, as you will hardly know which db to query to get certain records unless you also keep a meta database. Even then you’ll still often have to query both databases and then merge the results by hooking into further WP hooks. You get the picture.