MongoDB: Can I have a delayed secondary that doesn't vote? I have a replica set setup with 1 Primary, 1 Secondary and 1 Arbiter; each on a different data center.

I want to add a delayed secondary to one of the existing data centers, but I don't want it to participate in any election decisions.

I still want to have a total of 3 votes, so if the data center that hosts the delayed secondary (plus another member) goes down, my replica set would still elect a primary. Is this possible?
A configuration with three voting nodes in different data centres plus an additional non-voting delayed secondary is definitely supported. This is actually a reasonable configuration in terms of satisying core availability requirements using the distributed voting nodes with additional hidden/non-voting nodes for special use cases. A delayed secondary should be always configured as hidden and priority 0, and may have 0 or 1 vote.

However, there is one important caveat with your deployment: you have three data-bearing nodes but one of those is delayed. This will be problematic if you want to use any write concern higher than the usual default (w:1 aka acknowledgement by the primary). In the event one of your non-delayed secondaries is unavailable, a higher write concern (eg w:2 or w:majority) could still be satisfied but the writes would have to wait for acknowledgement from a second data-bearing node which would have to be the delayed secondary.

A more robust configuration would be to replace the arbiter with a data-bearing secondary so that unavailability of any of the three voting nodes would still allow for acknowledgement of majority writes.