Can I hide the submit button based on field values from Salesforce?

Yes - you can.
here's a scenario:
Say that someone registers their contact details, receives an email with a link to an online test form and completes it. He then clicks the link again with the intention of re-taking the test. In this scenario, the connector would check to see if the filler has already completed the test and if so - it will display a message instead of the test questions the submit button will be hidden (or disabled).

in a nutshell, all you have to do is:
- Create a custom (boolean) field in Salesforce to indicate if the person had taken the test or not. true or false.
- In your form, add a Push integration, so when the person submits the form it will also update the boolean field in Salesforce with the value 'true'.
- in your form, add a Get integration that reads the data from salesforce and checks the person's identity, and if he has already taken the test.
- If the answer is no ( 'false') then show this person the test and the submit button.
- if the answer is yes ('true') then hide the test questions, show a message instead, and hide the submit button as well.

Watch how to show/hide fields in the form based on conditions
Watch how to enable/disable fields using conditions