Will a prepaid Samsung phone work without a MicroSD card?

Of course it will. The MicroSD (if the phone can accept one, not all do) has nothing to do with the operation of the phone, it is only for your personal use (e.g. storing photos).

Perhaps you were thinking of a SIM card instead of a MicroSD card. Phones that use SIM cards (most cellphones do) cannot work at all without the SIM card, because it provides the Subscriber Information that associates the physical phone with your account in the phone provider's computers.