Hi there @springstreet,
I think there may be a couple of workarounds for what you're trying to achieve.
1. Is it possible to modify the layout of a page when tables are hidden? As far as I know, it is not a feature as such.
2. I can see that is a "Maintain Space when hidden" under the Appearance >> Advanced table settings. I assume that this would allow for the page to be more dynamic? Not a lot. Currently when components are one over each other, the moment one is hidden the other one will occupy the space of the hidden component. You can avoid this from happening by using this option. I find it helpful for forms when you have conditional fields.
3. Is there any alternative to address my goal? Off the top of my head, I'm thinking you could have two containers, the first one with your search bar in the middle, and another one with a second search bar on top and your tables. Once you click search you can hide the first container and show the second one. You'll have to modify your query so that it can understand which search bar to use depending on which container is show/hidden (or a variable of sorts)