Yes but with some functional limits. You have to have version of the CME supporting SIP trunking (higher than 4.1).
First you have to create in 3CX 'shadow' extensions with numbers following those you have defined in CME. All 3CX extensions must to have the same SIP credentials (username/password) - in example below xxxxx
Next - your sip-ua section should looks like this:
sip-ua
authentication username xxxx password xxxx
mwi-server ipv4:<IP of 3CX server> expires 3600 port 5060 transport udp unsolicited
registrar ipv4:<IP of 3CX server> expires 3600
sip-server ipv4:<IP of 3CX server>
host-registrar
After you have to create dial peers, outgoing and incoming:
dial-peer voice <number> voip
destination-pattern 0T
voice-class codec 1
session protocol sipv2
session target sip-server
dtmf-relay rtp-nte sip-notify sip-kpml
ip qos dscp cs5 media
ip qos dscp cs4 signaling
no vad
dial-peer voice <number> voip
voice-class codec 1
voice-class sip dtmf-relay force rtp-nte
session protocol sipv2
session target sip-server
incoming called-number .%
dtmf-relay sip-notify sip-kpml
ip qos dscp cs5 media
ip qos dscp cs4 signaling
no vad
All CME extensions will by defalult register in 3CX. For those you not like to be connected - use no sip-register command.
Now you should have both CME and 3CX integrated both way. To reach 3CX you have to dial prefix '0'. From 3CX wyou have to dial CME/shadow extension number. Voice mail will notify CME phones with MWI lindicator on the handset, dialing 0999 you will have access to the individual mailbox.
Now the best way to have voice mail available for incoming callers is to redirect those calls to the 3CX using 0<extension> number from CME.. WIthout leading '0' all 3CX redirection rules will not work since only 'shadow' extension will be called. Dialing in CME <extension> call will skip 3CX. It is not easy but will work.
For PSTN connections the best way is to connect all lines to 3CX and use CME only as a set of phones. And finally the simplest way is to change firmware in phones to SIP and use only 3CX
