Yes. Slackware uses procmail as the local delivery agent (LDA) and is setup to deliver to local users in /var/spool/mail/user. Each user would need a local ~/.procmailrc file to tell procmail where the user's mail box is
I hope I have the format right. It's been a while since I made a similar conversion.
[EDIT] Thanks dive! You are correct in post #3. I delete the misleading info from my post. [/EDIT]