Not necessarily.
I've only given it a few minutes thought, but position and time data is really small, and easy to compress (you don't need to send anything while the user isn't moving the mouse). If it's sent in batches or over an already open websocket, it's not like it's using a ton of resources on the client.
Assuming all of their users (guessing a billion daily active users) are on desktop half of the time (a wildly incorrect assumption I'm sure), and the mouse position data is 1mb per person for the data you care about (which again, seems like a lot), that's 500tb.
For $25k you could store it all. That's nothing compared to the benefits of being able to identify bots on your platform.