I think you can but the key will be setting up the email to go out via an SMTP server instead of the client email system. If you use the normal send mail with attachment and no dialog setting I know at least MS Outlook wont send. This is to mimimize your PC from becoming a zombie spammer-- which, still might be a problem with an SMTP server but at least it will get out of Filemaker.
There are no problems using the server to send email overnight ( I do it with the schedules of medical doctors) but the server cannot generate PDFs.
So, I use a text field for the email body and I compose the text with all the scheduling data (time, name of patient, notes, etc.) and I send the mails via SMTP directly.
To get arround server schedule limitations, you can set up a robot file that your OS launches at a specified time. It then performs the needed script on the hosted file to save, attach and send the PDF.