Does Exchange have a chance to work if..

Webhost 1and1 does not support smarthosting. My company does not want me to create a public mx record (it will replace mx record for 1and1’s webmail) and our entire domain is internal.
I say no, but I am being told it was done before and now I’m losing my mind trying to figure out how. I can send email all day long, send and rec internally and access the outlook web mail (just to proove I have a connection). If anyone can figure this out I would be eternally grateful. Thank you