Technically, yes. Is it useful, no.
No. You need another node. This helps determine which host is unavailable in the case of a network partition, among other things.
The minimum recommended configuration for a replica set is a three member replica set with three data-bearing members: one primary and two secondary members. In some circumstances (such as you have a primary and a secondary but cost constraints prohibit adding another secondary), you may choose to include an arbiter. An arbiter participates in elections but does not hold data (i.e. does not provide data redundancy).