If I send someone a file do they need a PixtaSynapse account to receive it?

No they don't.   From your PixtaSynapse Inbox you can delegate file(s) to the file recipient to pick-up the file from your account.  Once this action is received, a unique link is generated by the PixtaSynapse system and included in the email.   When the recipient opens the email they simply click on that link to download the file.  The recipient only will see the files that you delegated to them, no others.