Can users in the EU fill out and submit forms on a US based server?

Yes, they should. If they're from EU and they want to submit a form that is stored in US server, it should be fine. However, do take note that their data will be stored on US server since the form is hosted on US server.

If you are also from EU, you can decide if you want to store your form submissions back data to US server. By default, for all EU users, they are stored on EU server in order to comply with the safe harbour - EU rules.

To do that, go to your my accounts page, under settings simply uncheck the "Europe Datacenter".

If you have further questions, let us know.