I am curious, does Pokémon GO have its data saved on the phone, or is it stored on the web somewhere?
If I were to delete the app and reinstall it, would I have to start from the beginning again at level 1?
Pokemon Go is a client server based application, so you can reinstall the app as necessary.
This means that all the data is stored in the 'cloud' not on your device. Because of this, you can safely clear the data, remove the app or do whatever you need to (reset your phone to factory settings) and still be able to log back into the game and have your current game status right where you left it. In fact, in the first week of Pokemon Go being released I had to clear the application data several times on order to log back in to the game (it seems to be a lot more stable now though).
To back this up, here is a link to the server status' for the currently available Pokemon Go servers as per their region http://www.mmoserverstatus.com/pokemon_go
You can safely clear the data.
All game data outside of very immediate transactions is stored on the servers.
I've cleared my personal data several times but I don't think it does anything except reset options and credentials.