Is there a way to see how many downline referrals I have made, even if I have made no sales?

Yes, you can go to "Email Members" tab to see your downline members (if any)
 
Note that if you are a paid member you also have access to your own safe list mailing.

PLATINUM members can send email to MMT 50 members every 7 days (thats 1,400 members a month)
DIAMOND members can send email to MMT 75 members every 7 days (thats 2,100 members a month)
ELITE members can send email to MMT 100 members every 7 days (thats 2,800 members a month)