Hi Chesney, and welcome to the forum!
It’s definitely possible, and the good news is that it’s quite straightforward to do so 
Here’s a clone link for an app I just pulled together to demonstrate how it might work:
https://anvil.works/build#clone:GZR75BB7BFUBJB6O=I37PNFX57SLKM6AQ3QPIIXUU
I defined two server functions in my ServerModule, one that sends an email with the typeform link, and another that requests data from the typeform api.
The two Buttons in the UI trigger each of these server functions.
Since the typeform api requires you to send your personal access token as a header in the api request, I stored an ecrypted version of my personal token in my app using Anvil’s App Secrets service. I can then access my personal token in my server modules using anvil.secrets.get_secret('typeform_key')
At the moment, I’m just displaying the data returned from the api in a label - I’ll leave you to work through the JSON response and display the data in a more meaningful way.
Give it a go and let me know how you get on!