Along with the AN/APS-138 radar system, many of the E-2Cs featured:
(i) an electronic support measures (ESM) system to spot and locate radar and radio emitters, the system being designated the AN/ALR-73 Passive Detection System (PDS).
(ii) PDS antennas were also fitted on the endplate tailfins to give 360 degree coverage. The PDS covered four frequency bands and could track up to 250 emitters, characterizing them using a threat library.
These E-2Cs would later be known as the "Group 0" configuration. Singapore obtained 4x Group 0 E-2Cs, which went into operation in 1987. You are correct that an enemy plane should not be allowed to get within attack range of an E-2C, as they are high value assets. For more details on the E-2C see:
http://www.fas.org/programs/ssp/man/uswpns/air/special/e2c.html
As far as I am aware, Singapore's E-2Cs when they arrived 20 years ago were not armed and were possibly not equipped with countermeasures. It is possible that E-2Cs of that era are not even equipped with flares, as flares by themselves would not work (without other necessary countermeasures often found on fighter aircraft). However, IMHO, it is possible to fit a E-2C with modern countermeasures.
I also don't really see the point of arming as the AN/APS-138 radar system on the E-2C is not designed as an A2A missile targeting radar. I would assume that the AN/APS-138 radar system update rate would not be able to guide a AIM-120C missile into a position where the target is within the missile seeker's target acquisition basket. Therefore, the original E-2Cs are not armed.
Singapore's E-2C replacements are the
G550 CAEW and these new aircraft will come with countermeasures including an integrated self protection suite with 360° radar warning receiver (RWR), missile approach warning system (MAWS), chaff and flare decoy dispensers and directed infrared countermeasures (DIRCM).