PureEngage On-Premises

Is there a way to find the extension/DN that a teammate has logged into  based on only their Avaya user id?

Yes, this is possible by looking at the TServer / SIP Server logs and look for the following request:

The agent used in this example is IAllende

RequestAgentLogin

10:37:34.727 Trc 04541 RequestAgentLogin received from [528] (00000015 InteractionWorkspace_IAllende 139.56.123.64:3456)
message RequestAgentLogin
AttributeReferenceID 4
AttributePassword ''
AttributeThisDN '6001'
AttributeAgentWorkMode 0 (Unknown)
AttributeThisQueue '6601'
AttributeAgentID '1601'
 

Alternatively, you can also look for the event 'EventAgentReady' as shown below:

@10:37:34.7270 [0] 8.1.000.60 distribute_event: message EventAgentReady
AttributeExtensions [53] 00 01 00 00..
  'AgentSessionID' 'D8KI50GFS5245DR2GM3EQL25QK00005I'
AttributeEventSequenceNumber 00000000000002ab
AttributeTimeinuSecs 727000
AttributeTimeinSecs 1413553054 (10:37:34)
AttributeAgentWorkMode 0 (Unknown)
AttributeThisQueue '6601'
AttributeAgentID '1601'
AttributeThisDN '6001'
10:37:34.743 Trc 04542 EventAgentReady sent to [528] (00000015 InteractionWorkspace_IAllende 139.56.123.64:3456)

Is there a way to do it programmatically?  I have a custom application that the user logs into with their company username and pasword.  The application then queries Config Server for their Avaya id.  They are expected to also physically log into the hard phone with the same Avaya id.  I need to be able to find the place in Genesys TServer to connect to for this user.