Would I be able to email a client a questionnaire to complete?

Yes, you can email anyone and have anyone fill up your form if it is your intention.

Simply give them your form URL so they can view your form and fill it out.

Where-to-Find-My-Form-URL

However, I don't think they can fill out the form directly in Pages and Numbers. Nevertheless, you can add the form URL within your page/number.

On the other hand, since you are commenting from our Assign Form user guide, may I ask if you will be restricting form fill up to those whom you have specifically assigned only?

If yes, follow the steps here to assign your form:

Adding-assignees-to-your-form

Then modify each assignee's permission here:

Managing-permissions-for-your-assignees