Evite send to print

Is it a thing for me to make someone a bar mitzvah invitation and then they send it out to get professionally printed?

Yes, why not?

I would just send as a pdf with crop marks and bleed marks?

Looking at the title of your post - I didn’t realize you made it specifically for email, but if you think about it - it shouldn’t have been any cheaper than as if you were making it for print. The design work is the same.
Meaning - you’re making them an invitation, whatever they choose to do with it is irrelevant to how much you charge, no?